Finite Group Databasebeta

← C4×#11718651 #15784082

Subgroups — C4×#11718651 #15784082

Order 3328.

2134 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718651C212yesmaximal
2C2×C4×#6103C211yesmaximal, characteristic
3C2×C4×#6103C211yesmaximal, characteristic
4C2×C4×#6103C211yesmaximal, characteristic
5C2×C42×Dic13C211yesmaximal, characteristic, complemented
6#13113072C212yesmaximal
7#13113068C212yesmaximal, complemented
8#13113062C212yesmaximal, complemented
9C4×#88071C211yesmaximal, characteristic, complemented
10C4×#88071C211yesmaximal, characteristic, complemented
11C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C13×C4⋊C4C2212yes—
14C22×C42×C13C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×C42×C13C2211yescharacteristic
17C22×#6103C2212yes—
18C22×#6103C2212yes—
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C22×C4×Dic13C2212yes—
23C22×C4×Dic13C2211yescharacteristic
24C22×C4×Dic13C2212yes—
25C22×C4×Dic13C2211yescharacteristic
26C4×C13×C4⋊C4—24no—
27C2×C13×#95C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2211yescharacteristic
33C2×#88071C2211yescharacteristic
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36#11718651C4116yesdirect product factor
37C4×#6103—24no—
38C4×#6103—24no—
39C4×#6103C418yescomplemented
40C42×Dic13—24no—
41C24×D13C2311yescharacteristic
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2312yes—
46C23×C4×C13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2312yes—
51C23×Dic13C2311yescharacteristic
52C22×C4×D13—22no—
53C22×C4×D13—22no—
54C22×C4×D13—22no—
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13—22no—
58C22×C4×D13C2×C414yes—
59C2×C13×C4⋊C4—24no—
60C2×C13×C4⋊C4—24no—
61C2×C13×C4⋊C4C2×C418yescomplemented
62C2×C42×C13—22no—
63C2×C42×C13—22no—
64C2×C42×C13—22no—
65C2×C42×C13—22no—
66C2×C42×C13—22no—
67C2×C42×C13—22no—
68C2×C42×C13—22no—
69C2×C42×C13C2×C414yes—
70C2×C42×C13D414yes—
71C2×#6103—24no—
72C2×#6103—24no—
73C2×#6103—24no—
74C2×#6103—24no—
75C2×#6103—24no—
76C2×#6103C2×C414yes—
77C2×#6103C2×C418yes—
78C2×#6103C2×C418yes—
79C2×#6103C2×C414yes—
80C2×#6103C2×C418yes—
81C2×C4×Dic13—22no—
82C2×C4×Dic13—24no—
83C2×C4×Dic13—22no—
84C2×C4×Dic13—22no—
85C2×C4×Dic13—22no—
86C2×C4×Dic13—24no—
87C2×C4×Dic13—24no—
88C2×C4×Dic13—24no—
89C2×C4×Dic13—24no—
90C2×C4×Dic13—22no—
91C2×C4×Dic13—22no—
92C2×C4×Dic13—22no—
93C2×C4×Dic13C2×C414yes—
94C2×C4×Dic13C2×C418yescomplemented
95C2×C4×Dic13D414yes—
96C13×#95—24no—
97#88071—24no—
98#88071—24no—
99#88071—24no—
100#88071—24no—
101#88071C2×C414yes—
102#88071C2×C414yes—
103#88071C2×C418yescomplemented
104#88071C2×C418yescomplemented
105C4×#388—131nomaximal, Sylow
106C24×C13C2411yescharacteristic
107C23×D13—21no—
108C23×D13—21no—
109C23×D13—22no—
110C23×D13—22no—
111C23×D13—22no—
112C23×D13—21no—
113C23×D13—21no—
114C23×D13—21no—
115C23×D13—21no—
116C23×D13C22×C414yes—
117C23×D13C22×C412yes—
118C22×C4×C13—22no—
119C22×C4×C13—21no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—21no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—21no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—21no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13C22×C412yes—
136C22×C4×C13C22×C414yes—
137C22×C4×C13C22×C412yes—
138C22×C4×C13C22×C414yes—
139C22×C4×C13C22×C414yes—
140C22×C4×C13C22×C412yes—
141C22×C4×C13C2×D412yes—
142C22×C4×C13C2×D414yes—
143C22×C4×C13C2×D412yes—
144C22×C4×C13#4114yes—
145C22×C4×C13#4112yes—
146C22×C4×C13#4112yes—
147C22×C4×C13#4112yes—
148C22×C4×C13#4112yes—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—22no—
153C22×Dic13—21no—
154C22×Dic13—22no—
155C22×Dic13—22no—
156C22×Dic13—22no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13C22×C412yes—
172C22×Dic13C22×C414yes—
173C22×Dic13C22×C412yes—
174C22×Dic13C22×C414yes—
175C22×Dic13C22×C412yes—
176C22×Dic13C22×C414yes—
177C22×Dic13C2×D414yes—
178C22×Dic13#4114yes—
179C22×Dic13#4114yes—
180C2×C4×D13—28no—
181C2×C4×D13—28no—
182C2×C4×D13—28no—
183C2×C4×D13—44no—
184C2×C4×D13—44no—
185C2×C4×D13—44no—
186C2×C4×D13—44no—
187C13×C4⋊C4—216no—
188C42×C13—28no—
189C42×C13—28no—
190C42×C13—44no—
191#6103—216no—
192#6103—28no—
193#6103—216no—
194#6103C42116yescomplemented
195C4×Dic13—216no—
196C4×Dic13—28no—
197C4×Dic13—28no—
198C4×Dic13—216no—
199C4×Dic13—44no—
200C2×#388—132no—
201C2×C4×C4⋊C4D1311yescharacteristic, complemented
202C2×C4×C22⋊C4—131no—
203C2×C4×C22⋊C4—131no—
204C2×C4×C22⋊C4—131no—
205C2×C43—131no—
206#1437—132no—
207#1436—132no—
208#1434—132no—
209C4×#95—131no—
210C4×#95—131no—
211C23×C13C23×C411yescharacteristic
212C23×C13C23×C412yes—
213C23×C13C22×D411yescharacteristic
214C23×C13C22×D411yescharacteristic
215C23×C13C2×#4111yescharacteristic
216C23×C13C2×#4111yescharacteristic
217C23×C13C2×#4112yes—
218C23×C13C2×#4111yescharacteristic
219C23×C13C2×#4112yes—
220C23×C13C2×#4111yescharacteristic
221C23×C13C2×#4112yes—
222C22×D13—22no—
223C22×D13—22no—
224C22×D13—24no—
225C22×D13—24no—
226C22×D13—22no—
227C22×D13—22no—
228C22×D13—24no—
229C22×D13—24no—
230C22×D13—24no—
231C22×D13—24no—
232C22×D13—22no—
233C22×D13—22no—
234C22×D13—41no—
235C22×D13—41no—
236C22×D13—42no—
237C22×D13—41no—
238C22×D13—41no—
239C22×D13—42no—
240C22×D13—42no—
241C22×D13—42no—
242C22×D13—42no—
243C22×D13—42no—
244C22×D13C2×C4214yes—
245C2×C4×C13—24no—
246C2×C4×C13—22no—
247C2×C4×C13—24no—
248C2×C4×C13—24no—
249C2×C4×C13—22no—
250C2×C4×C13—24no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—24no—
254C2×C4×C13—24no—
255C2×C4×C13—22no—
256C2×C4×C13—24no—
257C2×C4×C13—22no—
258C2×C4×C13—24no—
259C2×C4×C13—22no—
260C2×C4×C13—24no—
261C2×C4×C13—42no—
262C2×C4×C13—42no—
263C2×C4×C13—42no—
264C2×C4×C13—42no—
265C2×C4×C13—42no—
266C2×C4×C13—42no—
267C2×C4×C13C2×C4214yes—
268C2×C4×C13#11714yes—
269C2×C4×C13C4×D418yes—
270C2×C4×C13C4×D414yes—
271C2×C4×C13C4×D414yes—
272C2×C4×C13#12114yes—
273C2×C4×C13#12314yes—
274C2×C4×C13#12414yes—
275C2×C4×C13#12614yes—
276C2×Dic13—22no—
277C2×Dic13—24no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—24no—
281C2×Dic13—22no—
282C2×Dic13—24no—
283C2×Dic13—24no—
284C2×Dic13—24no—
285C2×Dic13—24no—
286C2×Dic13—24no—
287C2×Dic13—24no—
288C2×Dic13—24no—
289C2×Dic13—24no—
290C2×Dic13—22no—
291C2×Dic13—24no—
292C2×Dic13—22no—
293C2×Dic13—22no—
294C2×Dic13—24no—
295C2×Dic13—24no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—42no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301C2×Dic13—42no—
302C2×Dic13—42no—
303C2×Dic13—42no—
304C2×Dic13C2×C4214yes—
305C2×Dic13#11714yes—
306C2×Dic13C4×D418yes—
307C4×D13—416no—
308C24×C4—131no—
309C22×C4⋊C4C2×D1312yes—
310C22×C22⋊C4—131no—
311C22×C22⋊C4—131no—
312C22×C22⋊C4—132no—
313C22×C22⋊C4—132no—
314C22×C42—132no—
315C22×C42—131no—
316C22×C42—131no—
317C22×C42—132no—
318C22×C42—131no—
319C22×C42C2×D1311yescharacteristic
320C22×C42C2×D1311yescharacteristic
321C22×C42C2×D1311yescharacteristic
322#388—1316no—
323C4×C4⋊C4—24no—
324C4×C22⋊C4—138no—
325C4×C22⋊C4—264no—
326C4×C22⋊C4—264no—
327C2×#95—132no—
328C2×#95—132no—
329C2×#95—131no—
330C2×#95—131no—
331C2×#95—132no—
332C2×#95—132no—
333C2×#95—132no—
334C2×#95—132no—
335C2×#95C2×D1312yes—
336C43—264no—
337C22×C13C22×C4211yescharacteristic
338C22×C13C2×#11711yescharacteristic
339C22×C13C2×#11711yescharacteristic
340C22×C13C2×C4×D411yescharacteristic
341C22×C13C2×C4×D411yescharacteristic
342C22×C13C2×C4×D412yes—
343C22×C13C2×C4×D412yes—
344C22×C13C4×#4112yes—
345C22×C13C4×#4111yescharacteristic
346C22×C13C4×#4111yescharacteristic
347C22×C13C4×#4112yes—
348C22×C13C4×#4112yes—
349C22×C13C4×#4112yes—
350C22×C13C2×#12111yescharacteristic
351C22×C13C2×#12311yescharacteristic
352C22×C13#52512yes—
353C22×C13C2×#12411yescharacteristic
354C22×C13C2×#12611yescharacteristic
355C22×C13#52912yes—
356C22×C13#52912yes—
357C22×C13#52912yes—
358C22×C13#52912yes—
359C22×C13#53212yes—
360C2×D13—24no—
361C2×D13—24no—
362C2×D13—24no—
363C2×D13—44no—
364C2×D13—42no—
365C2×D13—42no—
366C2×D13—42no—
367C2×D13—42no—
368C2×D13—44no—
369C2×D13—44no—
370C2×D13—44no—
371C4×C13—24no—
372C4×C13—28no—
373C4×C13—42no—
374C4×C13—44no—
375C4×C13#38818yescomplemented
376Dic13—24no—
377Dic13—24no—
378Dic13—28no—
379Dic13—42no—
380Dic13—44no—
381C25—131no—
382C23×C4—131no—
383C23×C4—132no—
384C23×C4—131no—
385C23×C4—132no—
386C23×C4—131no—
387C23×C4—134no—
388C23×C4—262no—
389C23×C4—262no—
390C23×C4—262no—
391C23×C4—262no—
392C23×C4—262no—
393C23×C4—262no—
394C23×C4C22×D1312yes—
395C23×C4C22×D1311yescharacteristic
396C23×C4C22×D1311yescharacteristic
397C23×C4C22×D1312yes—
398C23×C4C22×D1311yescharacteristic
399C2×C4⋊C4—24no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4C4×D1318yescomplemented
402C2×C22⋊C4—134no—
403C2×C22⋊C4—138no—
404C2×C22⋊C4—134no—
405C2×C22⋊C4—138no—
406C2×C22⋊C4—138no—
407C2×C22⋊C4—264no—
408C2×C22⋊C4—264no—
409C2×C22⋊C4—264no—
410C2×C22⋊C4—264no—
411C2×C22⋊C4—264no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—134no—
420C2×C42—138no—
421C2×C42—134no—
422C2×C42—264no—
423C2×C42—264no—
424C2×C42—264no—
425C2×C42—264no—
426C2×C42—264no—
427C2×C42—262no—
428C2×C42—262no—
429C2×C42—262no—
430C2×C42—262no—
431C2×C42—262no—
432C2×C42—262no—
433C2×C42—262no—
434C2×C42C4×D1314yes—
435C2×C42C22⋊D1314yes—
436#95—24no—
437#95—134no—
438#95—134no—
439#95—138no—
440#95—138no—
441#95—264no—
442#95—264no—
443#95—264no—
444#95—264no—
445C2×C13C4×#11711yescharacteristic
446C2×C13C42×D411yescharacteristic
447C2×C13C42×D411yescharacteristic
448C2×C13C2×#38811yescharacteristic
449C2×C13#229011yescharacteristic
450C2×C13#229311yescharacteristic
451C2×C13#229811yescharacteristic
452C2×C13C4×#12112yes—
453C2×C13C4×#12312yes—
454C2×C13C4×#12412yes—
455C2×C13C4×#12612yes—
456D13—44no—
457C24—134no—
458C24—132no—
459C24—262no—
460C24—261no—
461C24—261no—
462C24—261no—
463C24—261no—
464C24—261no—
465C24—262no—
466C24—262no—
467C24—261no—
468C24C23×D1311yescharacteristic
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—132no—
487C22×C4—134no—
488C22×C4—132no—
489C22×C4—134no—
490C22×C4—134no—
491C22×C4—134no—
492C22×C4—134no—
493C22×C4—134no—
494C22×C4—132no—
495C22×C4—262no—
496C22×C4—262no—
497C22×C4—262no—
498C22×C4—261no—
499C22×C4—261no—
500C22×C4—261no—
501C22×C4—261no—
502C22×C4—262no—
503C22×C4—262no—
504C22×C4—262no—
505C22×C4—262no—
506C22×C4—261no—
507C22×C4—261no—
508C22×C4—261no—
509C22×C4—262no—
510C22×C4—262no—
511C22×C4—261no—
512C22×C4—261no—
513C22×C4—262no—
514C22×C4—262no—
515C22×C4—261no—
516C22×C4—262no—
517C22×C4—268no—
518C22×C4—268no—
519C22×C4—268no—
520C22×C4—524no—
521C22×C4—524no—
522C22×C4—524no—
523C22×C4—524no—
524C22×C4C2×C4×D1312yes—
525C22×C4C2×C4×D1314yes—
526C22×C4C2×C4×D1312yes—
527C22×C4C2×C4×D1314yes—
528C22×C4C2×C4×D1314yes—
529C22×C4C2×C4×D1312yes—
530C22×C4#612714yes—
531C22×C4#612712yes—
532C22×C4D4×D1312yes—
533C22×C4#612912yes—
534C22×C4#613112yes—
535C22×C4#613112yes—
536C22×C4C2×C22⋊D1314yes—
537C22×C4C2×C22⋊D1312yes—
538C4⋊C4—216no—
539C22⋊C4—1316no—
540C22⋊C4—268no—
541C22⋊C4—2616no—
542C22⋊C4—2616no—
543C42—28no—
544C42—28no—
545C42—44no—
546C42—2616no—
547C42—2616no—
548C42—268no—
549C42—268no—
550C42—524no—
551C13C4×#38811yescharacteristic, complemented, Sylow
552C23—134no—
553C23—262no—
554C23—264no—
555C23—262no—
556C23—262no—
557C23—262no—
558C23—262no—
559C23—264no—
560C23—262no—
561C23—264no—
562C23—264no—
563C23—264no—
564C23—264no—
565C23—521no—
566C23—521no—
567C23—522no—
568C23—522no—
569C23—521no—
570C23—522no—
571C23—521no—
572C23—522no—
573C23—522no—
574C23—522no—
575C23C22×C4×D1311yescharacteristic
576C23C22×C4×D1312yes—
577C23C2×#612711yescharacteristic
578C23C2×#612712yes—
579C23C2×D4×D1311yescharacteristic
580C23C2×#612911yescharacteristic
581C23C2×#613111yescharacteristic
582C23C2×#613111yescharacteristic
583C23#41×D1312yes—
584C23#41×D1312yes—
585C23C22×C22⋊D1311yescharacteristic
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—134no—
609C2×C4—134no—
610C2×C4—138no—
611C2×C4—262no—
612C2×C4—264no—
613C2×C4—262no—
614C2×C4—262no—
615C2×C4—264no—
616C2×C4—262no—
617C2×C4—264no—
618C2×C4—264no—
619C2×C4—264no—
620C2×C4—264no—
621C2×C4—264no—
622C2×C4—264no—
623C2×C4—264no—
624C2×C4—264no—
625C2×C4—262no—
626C2×C4—262no—
627C2×C4—264no—
628C2×C4—262no—
629C2×C4—264no—
630C2×C4—264no—
631C2×C4—521no—
632C2×C4—521no—
633C2×C4—521no—
634C2×C4—522no—
635C2×C4—521no—
636C2×C4—522no—
637C2×C4—522no—
638C2×C4—522no—
639C2×C4—5216no—
640C2×C4C42×D1314yes—
641C2×C4#8814614yes—
642C2×C4#8814714yes—
643C2×C4#8814814yes—
644C2×C4#8815214yes—
645C2×C4C4×C22⋊D1318yes—
646C2×C4C4×C22⋊D1314yes—
647C2×C4#8819314yes—
648C2×C4#8820114yes—
649C22—264no—
650C22—264no—
651C22—264no—
652C22—522no—
653C22—522no—
654C22—522no—
655C22—522no—
656C22—524no—
657C22—524no—
658C22—524no—
659C22—524no—
660C22C2×C42×D1311yescharacteristic
661C22C4×#612711yescharacteristic
662C22C4×#612712yes—
663C22C2×#8814611yescharacteristic
664C22C2×#8814711yescharacteristic
665C22C2×#8814811yescharacteristic
666C22C2×#8815211yescharacteristic
667C22D13×#11711yescharacteristic
668C22#1171922711yescharacteristic
669C22#1171923312yes—
670C22C4×#612912yes—
671C22#1171924312yes—
672C22C4×D4×D1312yes—
673C22#1171925212yes—
674C22C4×#613112yes—
675C22C4×#613112yes—
676C22#1171928512yes—
677C22#1171928512yes—
678C22C2×C4×C22⋊D1311yescharacteristic
679C22C2×C4×C22⋊D1312yes—
680C22C2×#8819311yescharacteristic
681C22C2×#8820111yescharacteristic
682C22#1171953712yes—
683C4—28no—
684C4—24no—
685C4—42no—
686C4—44no—
687C4—264no—
688C4—268no—
689C4—264no—
690C4—522no—
691C4—524no—
692C4#1171865118yesdirect product factor
693C2—524no—
694C2C4×#8814611yescharacteristic
695C2C4×#8814711yescharacteristic
696C2C42×C22⋊D1311yescharacteristic
697C2C2×#1171865111yescharacteristic
698C2#1311727711yescharacteristic
699C2#1311729511yescharacteristic
700C2#1311732911yescharacteristic
701C2C4×#8819312yes—
702C2C4×#8814812yes—
703C2C4×#8820112yes—
704C2C4×#8815212yes—
subgroupG/H
centerC23×C4C22×D13
commutatorC22×C13C22×C42
FrattiniC24C23×D13
FittingC2×C4×C13×C4⋊C4C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×C4×C4⋊C4D13
hypocenterC13C4×#388
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
5. C2×C42×Dic13C2semidirect
7. #13113068C2semidirect
8. #13113062C2semidirect
9. C4×#88071C2semidirect
10. C4×#88071C2semidirect
11. C2×C4×C13×C4⋊C4C2semidirect
36. #11718651C4direct (N × H)
39. C4×#6103C4semidirect
61. C2×C13×C4⋊C4C2×C4semidirect
94. C2×C4×Dic13C2×C4semidirect
103. #88071C2×C4semidirect
104. #88071C2×C4semidirect
194. #6103C42semidirect
201. C2×C4×C4⋊C4D13semidirect
375. C4×C13#388semidirect
401. C2×C4⋊C4C4×D13semidirect
551. C13C4×#388semidirect
692. C4#11718651direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117186512
C2×C4×#61032
C2×C42×Dic132
#131130722
#131130682
#131130622
C4×#880712
C2×C4×C13×C4⋊C42
C4×#38813