Finite Group Databasebeta

← C2×#13120907 #16029587

Subgroups — C2×#13120907 #16029587

Order 3328.

1962 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120907C2116yesmaximal, direct product factor
2C2×#11718321C211yesmaximal, characteristic, complemented
3C2×#11718319C211yesmaximal, characteristic, complemented
4C2×#11718653C211yesmaximal, characteristic
5C2×#11718641C211yesmaximal, characteristic, complemented
6C2×#11718336C211yesmaximal, characteristic
7C2×#11718654C211yesmaximal, characteristic
8C2×#11718655C211yesmaximal, characteristic
9C2×#11718633C211yesmaximal, characteristic, complemented
10C2×#11718331C211yesmaximal, characteristic
11C2×#11718651C211yesmaximal, characteristic
12C2×#11718330C211yesmaximal, characteristic
13C2×#11718642C211yesmaximal, characteristic, complemented
14C2×#11718314C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
16C2×C13×#398C211yesmaximal, characteristic, complemented
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×#6101C2211yescharacteristic
33C22×#6101C2211yescharacteristic
34C22×#6101C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C22×C4×Dic13C2211yescharacteristic
37C22×C4×Dic13C2211yescharacteristic
38C13×#398C2218yescomplemented
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41C2×C13×#95C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53#11718655C2218yes—
54#11718654C2218yes—
55#11718653C2218yes—
56#11718651C2218yes—
57#11718642C2218yescomplemented
58#11718641C2218yescomplemented
59C4⋊C4×Dic13C2218yescomplemented
60#11718633C2218yescomplemented
61#11718336C2218yes—
62#11718331C2218yes—
63#11718330C2218yes—
64#11718321C2218yescomplemented
65#11718319C2218yescomplemented
66#11718314C2218yescomplemented
67C24×D13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C2×C13×C4⋊C4—24no—
83C2×C13×C4⋊C4—24no—
84C2×C13×C4⋊C4—42no—
85C2×C13×C4⋊C4—42no—
86C2×C13×C4⋊C4C2314yes—
87C2×C13×C4⋊C4C2314yes—
88C2×C13×C4⋊C4C2314yes—
89C2×C13×C4⋊C4C2314yes—
90C2×#6103—24no—
91C2×#6103—24no—
92C2×#6103—24no—
93C2×#6103—42no—
94C2×#6103—42no—
95C2×#6103—42no—
96C2×#6103—42no—
97C2×#6103C2314yes—
98C2×#6103C2314yes—
99C2×#6103C2314yes—
100C2×#6103C2314yes—
101C2×#6103C2314yes—
102C2×#6103C2314yes—
103C2×#6103C2314yes—
104C2×C4⋊Dic13—24no—
105C2×C4⋊Dic13—24no—
106C2×C4⋊Dic13C2314yes—
107C2×C4⋊Dic13C2314yes—
108C2×#6101—24no—
109C2×#6101—42no—
110C2×#6101—42no—
111C2×#6101—42no—
112C2×#6101—42no—
113C2×#6101C2314yes—
114C2×#6101C2314yes—
115C2×#6101C2314yes—
116C2×#6101C2314yes—
117C2×#6101C2314yes—
118C2×C4×Dic13—24no—
119C2×C4×Dic13—42no—
120C2×C4×Dic13—42no—
121C2×C4×Dic13C2314yes—
122C2×C4×Dic13C2314yes—
123C2×C4×Dic13C2314yes—
124C13×#95C2314yes—
125C13×#95C2314yes—
126C13×#95C2314yes—
127#88071C2314yes—
128#88071C2314yes—
129#88071C2314yes—
130#88071C2314yes—
131#88071C2314yes—
132#88071C2314yes—
133#88071C2314yes—
134#88071C2314yes—
135#88071C2314yes—
136#88071C2314yes—
137#88071C2314yes—
138C2×#2654—131nomaximal, Sylow
139C24×C13C2411yescharacteristic
140C23×D13—22no—
141C23×D13—22no—
142C23×D13—22no—
143C23×D13—22no—
144C23×D13—22no—
145C23×D13—22no—
146C23×D13—22no—
147C23×D13C2412yes—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13#4114yes—
169C22×C4×C13C2412yes—
170C22×C4×C13C2412yes—
171C22×C4×C13C2412yes—
172C22×C4×C13C2412yes—
173C22×C4×C13C2412yes—
174C22×C4×C13C2412yes—
175C22×C4×C13C2412yes—
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13#4114yes—
196C22×Dic13#4114yes—
197C22×Dic13C2412yes—
198C22×Dic13C2412yes—
199C22×Dic13C2412yes—
200C22×Dic13C2412yes—
201C22×Dic13C2412yes—
202C22×Dic13C2412yes—
203C22×Dic13C2412yes—
204C13×C4⋊C4—28no—
205C13×C4⋊C4—28no—
206C13×C4⋊C4—44no—
207C13×C4⋊C4—44no—
208#6103—28no—
209#6103—28no—
210#6103—28no—
211#6103—44no—
212#6103—44no—
213#6103—44no—
214#6103—44no—
215C4⋊Dic13—28no—
216C4⋊Dic13—28no—
217#6101—28no—
218#6101—44no—
219#6101—44no—
220#6101—44no—
221#6101—44no—
222C4×Dic13—28no—
223C4×Dic13—44no—
224C4×Dic13—44no—
225#2654—1316no—
226C2×#400—131no—
227C2×#400—131no—
228C2×#399—131no—
229C2×#398—131no—
230C2×#398D1311yescharacteristic, complemented
231C2×#397—131no—
232C2×#397—131no—
233C2×#396—131no—
234C2×#389—131no—
235C2×#388—131no—
236C2×#388—131no—
237C2×#388—131no—
238C2×#387—131no—
239C2×#387—131no—
240C2×C4×C4⋊C4—131no—
241C23×C13C2×#4112yes—
242C23×C13C2×#4112yes—
243C23×C13C2×#4112yes—
244C23×C13H(5,𝔽2)12yes—
245C23×C13H(5,𝔽2)12yes—
246C23×C132−1+412yes—
247C23×C132−1+412yes—
248C23×C13C2511yescharacteristic
249C22×D13—22no—
250C22×D13—22no—
251C22×D13—22no—
252C22×D13—22no—
253C22×D13—22no—
254C22×D13—22no—
255C22×D13—22no—
256C22×D13—44no—
257C22×D13—44no—
258C22×D13—44no—
259C22×D13—44no—
260C22×D13—44no—
261C22×D13—44no—
262C22×D13—44no—
263C2×C4×C13—28no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—22no—
267C2×C4×C13—22no—
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—22no—
271C2×C4×C13—22no—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—44no—
285C2×C4×C13—44no—
286C2×C4×C13—44no—
287C2×C4×C13—44no—
288C2×C4×C13—44no—
289C2×C4×C13—44no—
290C2×C4×C13C2×#4114yes—
291C2×Dic13—28no—
292C2×Dic13—28no—
293C2×Dic13—22no—
294C2×Dic13—22no—
295C2×Dic13—22no—
296C2×Dic13—22no—
297C2×Dic13—22no—
298C2×Dic13—22no—
299C2×Dic13—22no—
300C2×Dic13—22no—
301C2×Dic13—22no—
302C2×Dic13—22no—
303C2×Dic13—22no—
304C2×Dic13—22no—
305C2×Dic13—22no—
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—44no—
313C2×Dic13—44no—
314C2×Dic13—44no—
315C2×Dic13—44no—
316C2×Dic13—44no—
317C2×Dic13C2×#4114yes—
318C2×Dic13C2×#4114yes—
319C22×C4⋊C4—131no—
320C22×C4⋊C4—131no—
321C22×C4⋊C4—131no—
322C22×C4⋊C4—131no—
323C22×C4⋊C4—131no—
324C22×C4⋊C4—131no—
325C22×C4⋊C4—131no—
326C22×C4⋊C4C2×D1311yescharacteristic
327C22×C4⋊C4C2×D1311yescharacteristic
328C22×C4⋊C4C2×D1311yescharacteristic
329C22×C4⋊C4C2×D1311yescharacteristic
330C22×C22⋊C4—131no—
331C22×C22⋊C4—131no—
332C22×C22⋊C4—131no—
333C22×C22⋊C4—131no—
334C22×C22⋊C4—131no—
335C22×C22⋊C4—131no—
336C22×C22⋊C4—131no—
337C22×C42—131no—
338C22×C42—131no—
339C22×C42—131no—
340#400—138no—
341#400—138no—
342#399—138no—
343#398—138no—
344#398C2×D1318yescomplemented
345#397—138no—
346#397—138no—
347#396—138no—
348#389—138no—
349#388—138no—
350#388—138no—
351#388—138no—
352#387—138no—
353#387—138no—
354C4×C4⋊C4—138no—
355C2×#95—131no—
356C2×#95—131no—
357C2×#95—131no—
358C2×#95—131no—
359C2×#95—131no—
360C2×#95—131no—
361C2×#95—131no—
362C2×#95—131no—
363C2×#95—131no—
364C2×#95—131no—
365C2×#95—131no—
366C2×#95C2×D1311yescharacteristic
367C2×#95C2×D1311yescharacteristic
368C2×#95C2×D1311yescharacteristic
369C22×C13#52914yes—
370C22×C13#53914yes—
371C22×C13#53914yes—
372C22×C13#54014yes—
373C22×C13#54114yes—
374C22×C13#54214yes—
375C22×C13#54214yes—
376C22×C13C22×#4111yescharacteristic
377C22×C13C22×#4111yescharacteristic
378C22×C13C22×#4111yescharacteristic
379C22×C13C2×H(5,𝔽2)11yescharacteristic
380C22×C13C2×H(5,𝔽2)11yescharacteristic
381C22×C13C2×2−1+411yescharacteristic
382C22×C13C2×2−1+411yescharacteristic
383C2×D13—42no—
384C2×D13—42no—
385C2×D13—42no—
386C2×D13—42no—
387C2×D13—42no—
388C2×D13—42no—
389C2×D13—42no—
390C2×D13—88no—
391C4×C13—24no—
392C4×C13—42no—
393C4×C13—42no—
394C4×C13—42no—
395C4×C13—42no—
396C4×C13—42no—
397C4×C13—42no—
398Dic13—24no—
399Dic13—24no—
400Dic13—42no—
401Dic13—42no—
402Dic13—42no—
403Dic13—42no—
404Dic13—42no—
405C25—131no—
406C23×C4—131no—
407C23×C4—131no—
408C23×C4—131no—
409C23×C4—131no—
410C23×C4—131no—
411C23×C4—131no—
412C23×C4—131no—
413C23×C4C22×D1311yescharacteristic
414C23×C4C22×D1311yescharacteristic
415C23×C4C22×D1311yescharacteristic
416C23×C4C22×D1311yescharacteristic
417C23×C4C22×D1311yescharacteristic
418C23×C4C22×D1311yescharacteristic
419C23×C4C22×D1311yescharacteristic
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—134no—
425C2×C4⋊C4—134no—
426C2×C4⋊C4—134no—
427C2×C4⋊C4—134no—
428C2×C4⋊C4—134no—
429C2×C4⋊C4—134no—
430C2×C4⋊C4—134no—
431C2×C4⋊C4—264no—
432C2×C4⋊C4—264no—
433C2×C4⋊C4—264no—
434C2×C4⋊C4—522no—
435C2×C4⋊C4—522no—
436C2×C4⋊C4—522no—
437C2×C4⋊C4—522no—
438C2×C4⋊C4C22×D1314yes—
439C2×C4⋊C4C22×D1314yes—
440C2×C4⋊C4C22×D1314yes—
441C2×C4⋊C4C22×D1314yes—
442C2×C22⋊C4—134no—
443C2×C22⋊C4—134no—
444C2×C22⋊C4—134no—
445C2×C22⋊C4—134no—
446C2×C22⋊C4—134no—
447C2×C22⋊C4—134no—
448C2×C22⋊C4—134no—
449C2×C22⋊C4—264no—
450C2×C22⋊C4—264no—
451C2×C22⋊C4—264no—
452C2×C22⋊C4—522no—
453C2×C22⋊C4—522no—
454C2×C22⋊C4—522no—
455C2×C22⋊C4—522no—
456C2×C42—134no—
457C2×C42—134no—
458C2×C42—134no—
459C2×C42—264no—
460C2×C42—522no—
461C2×C42—522no—
462#95—134no—
463#95—134no—
464#95—134no—
465#95—134no—
466#95—134no—
467#95—134no—
468#95—134no—
469#95—134no—
470#95—134no—
471#95—134no—
472#95—134no—
473#95C22×D1314yes—
474#95C22×D1314yes—
475#95C22×D1314yes—
476C2×C13#265418yescomplemented
477C2×C13C2×#52911yescharacteristic
478C2×C13C2×#53911yescharacteristic
479C2×C13C2×#53911yescharacteristic
480C2×C13C2×#54011yescharacteristic
481C2×C13C2×#54111yescharacteristic
482C2×C13C2×#54211yescharacteristic
483C2×C13C2×#54211yescharacteristic
484D13—82no—
485C24—132no—
486C24—262no—
487C24—262no—
488C24—262no—
489C24—262no—
490C24—262no—
491C24—262no—
492C24—262no—
493C24C23×D1311yescharacteristic
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—134no—
515C22×C4—134no—
516C22×C4—132no—
517C22×C4—132no—
518C22×C4—132no—
519C22×C4—132no—
520C22×C4—132no—
521C22×C4—132no—
522C22×C4—132no—
523C22×C4—262no—
524C22×C4—262no—
525C22×C4—262no—
526C22×C4—262no—
527C22×C4—262no—
528C22×C4—262no—
529C22×C4—262no—
530C22×C4—262no—
531C22×C4—262no—
532C22×C4—262no—
533C22×C4—262no—
534C22×C4—262no—
535C22×C4—262no—
536C22×C4—262no—
537C22×C4—262no—
538C22×C4—262no—
539C22×C4—262no—
540C22×C4—262no—
541C22×C4—262no—
542C22×C4#612914yes—
543C22×C4C23×D1312yes—
544C22×C4C23×D1312yes—
545C22×C4C23×D1312yes—
546C22×C4C23×D1312yes—
547C22×C4C23×D1312yes—
548C22×C4C23×D1312yes—
549C22×C4C23×D1312yes—
550C4⋊C4—28no—
551C4⋊C4—28no—
552C4⋊C4—44no—
553C4⋊C4—44no—
554C4⋊C4—268no—
555C4⋊C4—268no—
556C4⋊C4—268no—
557C4⋊C4—524no—
558C4⋊C4—524no—
559C4⋊C4—524no—
560C4⋊C4—524no—
561C22⋊C4—268no—
562C22⋊C4—268no—
563C22⋊C4—268no—
564C22⋊C4—524no—
565C22⋊C4—524no—
566C22⋊C4—524no—
567C22⋊C4—524no—
568C42—268no—
569C42—524no—
570C42—524no—
571C13C2×#265411yescharacteristic, complemented, Sylow
572C23—262no—
573C23—262no—
574C23—262no—
575C23—262no—
576C23—262no—
577C23—262no—
578C23—262no—
579C23—524no—
580C23—524no—
581C23—524no—
582C23—524no—
583C23—524no—
584C23—524no—
585C23—524no—
586C23C2×#612912yes—
587C23#8825112yes—
588C23#8825412yes—
589C23#8825412yes—
590C23#41×D1312yes—
591C23#41×D1312yes—
592C23#8825612yes—
593C23C24×D1311yescharacteristic
594C2×C4—28no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—44no—
618C2×C4—44no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—134no—
622C2×C4—134no—
623C2×C4—262no—
624C2×C4—262no—
625C2×C4—262no—
626C2×C4—262no—
627C2×C4—268no—
628C2×C4—268no—
629C2×C4—262no—
630C2×C4—262no—
631C2×C4—262no—
632C2×C4—262no—
633C2×C4—262no—
634C2×C4—262no—
635C2×C4—262no—
636C2×C4—262no—
637C2×C4—262no—
638C2×C4—262no—
639C2×C4—262no—
640C2×C4—262no—
641C2×C4—262no—
642C2×C4—262no—
643C2×C4—262no—
644C2×C4—524no—
645C2×C4—524no—
646C2×C4—524no—
647C2×C4—524no—
648C2×C4—524no—
649C2×C4C2×#612914yes—
650C22—522no—
651C22—522no—
652C22—522no—
653C22—522no—
654C22—522no—
655C22—522no—
656C22—522no—
657C22—1048no—
658C22#1171932414yes—
659C22#1171934514yes—
660C22#1171934514yes—
661C22#1171935414yes—
662C22#1171939714yes—
663C22#1171939714yes—
664C22#1171943614yes—
665C22C22×#612911yescharacteristic
666C22C2×#8825111yescharacteristic
667C22C2×#8825411yescharacteristic
668C22C2×#8825411yescharacteristic
669C22C2×#41×D1311yescharacteristic
670C22C2×#41×D1311yescharacteristic
671C22C2×#8825611yescharacteristic
672C4—24no—
673C4—42no—
674C4—42no—
675C4—42no—
676C4—42no—
677C4—42no—
678C4—42no—
679C4—264no—
680C4—264no—
681C4—522no—
682C4—522no—
683C4—522no—
684C4—522no—
685C4—522no—
686C2—1042no—
687C2#1312090718yesdirect product factor
688C2C2×#1171935411yescharacteristic
689C2C2×#1171939711yescharacteristic
690C2C2×#1171939711yescharacteristic
691C2C2×#1171932411yescharacteristic
692C2C2×#1171943611yescharacteristic
693C2C2×#1171934511yescharacteristic
694C2C2×#1171934511yescharacteristic
subgroupG/H
centerC24C23×D13
commutator, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC2×C13×#398C2
socleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#398D13
hypocenterC13C2×#2654
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#398

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13120907C2direct (N × H)
2. C2×#11718321C2semidirect
3. C2×#11718319C2semidirect
5. C2×#11718641C2semidirect
9. C2×#11718633C2semidirect
13. C2×#11718642C2semidirect
14. C2×#11718314C2semidirect
15. C2×C4⋊C4×Dic13C2semidirect
16. C2×C13×#398C2semidirect
38. C13×#398C22semidirect
57. #11718642C22semidirect
58. #11718641C22semidirect
59. C4⋊C4×Dic13C22semidirect
60. #11718633C22semidirect
64. #11718321C22semidirect
65. #11718319C22semidirect
66. #11718314C22semidirect
230. C2×#398D13semidirect
344. #398C2×D13semidirect
476. C2×C13#2654semidirect
571. C13C2×#2654semidirect
687. C2#13120907direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131209072
C2×#117183212
C2×#117183192
C2×#117186532
C2×#117186412
C2×#117183362
C2×#117186542
C2×#117186552
C2×#117186332
C2×#117183312
C2×#117186512
C2×#117183302
C2×#117186422
C2×#117183142
C2×C4⋊C4×Dic132
C2×C13×#3982
C2×#265413