Finite Group Databasebeta

← C2×#13127743 #16743405

Subgroups — C2×#13127743 #16743405

Order 3328.

1854 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719427C211yesmaximal, characteristic, complemented
2C2×#11719395C211yesmaximal, characteristic
3#13127743C2116yesmaximal, direct product factor
4C2×#11718517C211yesmaximal, characteristic, complemented
5C2×#11718535C211yesmaximal, characteristic, complemented
6C2×#11718518C211yesmaximal, characteristic, complemented
7C2×#11718724C211yesmaximal, characteristic, complemented
8C2×#11718536C211yesmaximal, characteristic, complemented
9C2×#11718531C211yesmaximal, characteristic
10C2×#11718551C211yesmaximal, characteristic
11C2×#11718748C211yesmaximal, characteristic
12C2×#11718362C211yesmaximal, characteristic, complemented
13C2×#11718371C211yesmaximal, characteristic
14C2×#11718550C211yesmaximal, characteristic
15C2×#11718513C211yesmaximal, characteristic
16C2×C13×#501C211yesmaximal, characteristic, complemented
17C2×C13×C4⋊Q8C2211yescharacteristic
18C2×C13×#125C2211yescharacteristic
19C2×#88198—21no—
20C2×#88198—21no—
21C22×#6095C2211yescharacteristic
22#11719427—24no—
23#11719427C2218yescomplemented
24#11719395—24no—
25#11719395C2218yes—
26C2×#88151—21no—
27C2×#88150—21no—
28C2×#88150—21no—
29C2×#88147C2211yescharacteristic
30C2×#88147C2211yescharacteristic
31C2×C4⋊C4×D13—21no—
32C2×#88144C2211yescharacteristic
33C2×#88142—21no—
34C2×#88142C2211yescharacteristic
35C2×#88142C2211yescharacteristic
36C2×#88142C2211yescharacteristic
37C2×#88141—21no—
38C2×#88141C2211yescharacteristic
39C2×#88141C2211yescharacteristic
40C2×C4×D52C2211yescharacteristic
41C2×C4×Dic26C2211yescharacteristic
42C2×C4×Dic26C2211yescharacteristic
43C13×#501C2218yescomplemented
44C2×C13×#107C2211yescharacteristic
45C2×C13×#107C2211yescharacteristic
46C2×C13×#106C2211yescharacteristic
47C2×C13×#106C2211yescharacteristic
48C2×C13×#97C2211yescharacteristic
49C2×#88061C2211yescharacteristic
50C2×#88058C2211yescharacteristic
51C2×#88056C2211yescharacteristic
52C2×#88055C2211yescharacteristic
53C2×#88054C2211yescharacteristic
54C2×#88054C2211yescharacteristic
55C2×C8×Dic13C2211yescharacteristic
56#11718748C2218yes—
57#11718724C2218yescomplemented
58C2×#88050C2211yescharacteristic
59C2×#88050C2211yescharacteristic
60C2×#88049C2211yescharacteristic
61C2×#88049C2211yescharacteristic
62C2×#88048C2211yescharacteristic
63C2×#88047C2211yescharacteristic
64C2×#88047C2211yescharacteristic
65C2×#88047C2211yescharacteristic
66C2×C4⋊#1055C2211yescharacteristic
67#11718551C2218yes—
68#11718550C2218yes—
69#11718536C2218yescomplemented
70#11718535C2218yescomplemented
71#11718531C2218yes—
72#11718518C2218yescomplemented
73#11718517C2218yescomplemented
74#11718513C2218yes—
75#11718371C2218yes—
76#11718362C2218yescomplemented
77C22×Q8×C13—21no—
78C22×D52C2311yescharacteristic
79C22×C4×D13—21no—
80C22×C4×D13—21no—
81C22×C4×D13—21no—
82C22×Dic26—21no—
83C22×Dic26—21no—
84C22×Dic26—21no—
85C22×Dic26D411yescharacteristic
86C22×Dic26C2311yescharacteristic
87C22×C8×C13C2311yescharacteristic
88C22×C8×C13C2311yescharacteristic
89C13×C4⋊Q8—22no—
90C13×C4⋊Q8C2314yes—
91C13×#125—22no—
92C13×#125C2314yes—
93C2×C13×C4⋊C4—21no—
94C2×C13×C4⋊C4—21no—
95C2×C13×C4⋊C4—21no—
96C2×C13×C4⋊C4C2311yescharacteristic
97C2×C13×C4⋊C4C2311yescharacteristic
98C2×C13×C4⋊C4C2311yescharacteristic
99C2×C13×C4⋊C4C2311yescharacteristic
100C2×C42×C13C2311yescharacteristic
101#88198—28no—
102#88198—28no—
103C2×#6103—21no—
104C2×#6103—21no—
105C2×#6103—21no—
106C2×C4⋊Dic13—21no—
107C2×C4⋊Dic13D411yescharacteristic
108C2×C4⋊Dic13C2311yescharacteristic
109C2×C4⋊Dic13C2311yescharacteristic
110C2×#6101—21no—
111C2×#6101—21no—
112C2×#6101—21no—
113C2×#6101—21no—
114C2×#6101—21no—
115C2×#6101—21no—
116C2×#6101—21no—
117C2×#6101D411yescharacteristic
118C2×#6101D411yescharacteristic
119C2×C4×Dic13—21no—
120C2×C4×Dic13—21no—
121C2×C4×Dic13—21no—
122C2×C4×Dic13C2311yescharacteristic
123C2×C4×Dic13C2311yescharacteristic
124C22×#1055C2311yescharacteristic
125C22×#1055C2311yescharacteristic
126C2×#6095Q818yescomplemented
127C2×#6095C2314yes—
128#88151—28no—
129#88150—28no—
130#88150—28no—
131#88147—22no—
132#88147—22no—
133#88147C2314yes—
134#88147C2314yes—
135C4⋊C4×D13—28no—
136#88144—22no—
137#88144C2314yes—
138#88142—28no—
139#88142—22no—
140#88142—22no—
141#88142—22no—
142#88142C2314yes—
143#88142C2314yes—
144#88142C2314yes—
145#88141—28no—
146#88141—22no—
147#88141—22no—
148#88141C2314yes—
149#88141C2314yes—
150C4×D52—22no—
151C4×D52C2314yes—
152C4×Dic26—22no—
153C4×Dic26D414yes—
154C4×Dic26C2314yes—
155C4×Dic26C2314yes—
156C13×#107C2314yes—
157C13×#107C2314yes—
158C13×#106C2314yes—
159C13×#106C2314yes—
160C13×#97C2314yes—
161#88061C2314yes—
162#88058C2314yes—
163#88056C2314yes—
164#88055C2314yes—
165#88054C2314yes—
166#88054C2314yes—
167C8×Dic13C2314yes—
168#88050C2314yes—
169#88050C2314yes—
170#88049C2314yes—
171#88049C2314yes—
172#88048C2314yes—
173#88047C2314yes—
174#88047C2314yes—
175#88047C2314yes—
176C4⋊#1055C2314yes—
177C2×#3385—131nomaximal, Sylow
178C23×D13—21no—
179C2×Q8×C13—24no—
180C2×Q8×C13—82no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13C2×D411yescharacteristic
186C22×C4×C13C2×D411yescharacteristic
187C22×C4×C13C2411yescharacteristic
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13C2×D411yescharacteristic
192C22×Dic13C2×D411yescharacteristic
193C22×Dic13C2×D411yescharacteristic
194C22×Dic13C2×D411yescharacteristic
195C2×D52—21no—
196C2×D52—22no—
197C2×D52C2×Q814yes—
198C2×D52C2412yes—
199C2×C4×D13—24no—
200C2×C4×D13—24no—
201C2×C4×D13—24no—
202C2×C4×D13—44no—
203C2×C4×D13—82no—
204C2×C4×D13—82no—
205C2×Dic26—21no—
206C2×Dic26—22no—
207C2×Dic26—24no—
208C2×Dic26—24no—
209C2×Dic26—24no—
210C2×Dic26—24no—
211C2×Dic26—82no—
212C2×Dic26—82no—
213C2×Dic26—82no—
214C2×Dic26C2×D414yes—
215C2×Dic26C2×Q814yes—
216C2×Dic26C2412yes—
217C2×C8×C13—22no—
218C2×C8×C13C2×Q814yes—
219C2×C8×C13C2412yes—
220C2×C8×C13C2412yes—
221C13×C4⋊C4—24no—
222C13×C4⋊C4—21no—
223C13×C4⋊C4—21no—
224C13×C4⋊C4—21no—
225C13×C4⋊C4—21no—
226C13×C4⋊C4—24no—
227C13×C4⋊C4—24no—
228C13×C4⋊C4C2412yes—
229C13×C4⋊C4C2412yes—
230C13×C4⋊C4C2412yes—
231C13×C4⋊C4C2412yes—
232C42×C13C2×D412yes—
233C42×C13C2412yes—
234#6103—24no—
235#6103—24no—
236#6103—24no—
237C4⋊Dic13—21no—
238C4⋊Dic13—21no—
239C4⋊Dic13—24no—
240C4⋊Dic13C2×D414yes—
241C4⋊Dic13C2412yes—
242C4⋊Dic13C2412yes—
243#6101—24no—
244#6101—24no—
245#6101—24no—
246#6101—24no—
247#6101—24no—
248#6101—24no—
249#6101—24no—
250#6101C2×D414yes—
251#6101C2×D414yes—
252C4×Dic13—24no—
253C4×Dic13—24no—
254C4×Dic13—24no—
255C4×Dic13C2×D412yes—
256C4×Dic13C2×D412yes—
257C4×Dic13C2412yes—
258C4×Dic13C2412yes—
259C2×#1055—22no—
260C2×#1055—22no—
261C2×#1055C2412yes—
262C2×#1055C2412yes—
263#6095C2×Q8116yescomplemented
264C2×Q82—131no—
265C2×#554—131no—
266#3385—1316no—
267C2×#501—131no—
268C2×#501D1311yescharacteristic, complemented
269C2×#500—131no—
270C2×#479—131no—
271C2×#479—131no—
272C2×#477—131no—
273C2×#476—131no—
274C2×#474—131no—
275C2×#474—131no—
276C2×#446—131no—
277C2×#440—131no—
278C2×#440—131no—
279C2×C4×SD16—131no—
280C23×C13C22×D411yescharacteristic
281C22×D13—24no—
282C22×D13—22no—
283C22×D13—42no—
284C22×D13—42no—
285Q8×C13—84no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—42no—
293C2×C4×C13—42no—
294C2×C4×C13—42no—
295C2×C4×C13—42no—
296C2×C4×C13C22×D412yes—
297C2×C4×C13C22×D412yes—
298C2×C4×C13C22×D411yescharacteristic
299C2×C4×C13C22×Q812yes—
300C2×C4×C132−1+412yes—
301C2×C4×C13C2511yescharacteristic
302C2×Dic13—24no—
303C2×Dic13—22no—
304C2×Dic13—22no—
305C2×Dic13—22no—
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—42no—
310C2×Dic13—42no—
311C2×Dic13#13714yes—
312C2×Dic13C22×D412yes—
313C2×Dic13C22×D412yes—
314C2×Dic13C22×D412yes—
315C2×Dic13C22×D412yes—
316D52—24no—
317D52—22no—
318D52C22×Q814yes—
319C4×D13—48no—
320C4×D13—84no—
321C4×D13—84no—
322Dic26—24no—
323Dic26—22no—
324Dic26—28no—
325Dic26—84no—
326Dic26—84no—
327Dic26—84no—
328Dic26C22×Q814yes—
329C8×C13—22no—
330C8×C13C22×Q814yes—
331#1055—22no—
332#1055—22no—
333C22×SD16—131no—
334Q82—138no—
335Q82—264no—
336#554—138no—
337#554—264no—
338C2×C4⋊Q8—131no—
339C2×C4⋊Q8—131no—
340C2×C4⋊Q8—131no—
341C2×C4⋊Q8—261no—
342C2×C4⋊Q8—261no—
343C2×C4⋊Q8—261no—
344C2×C4⋊Q8C2×D1311yescharacteristic
345C2×#125—131no—
346C2×#125C2×D1311yescharacteristic
347C2×C22⋊Q8—261no—
348C2×C22⋊Q8—261no—
349C2×C22⋊Q8—261no—
350C2×C4×Q8—131no—
351C2×C4×Q8—131no—
352C2×C4×Q8—131no—
353C2×C4×Q8—131no—
354C2×C4×Q8—261no—
355C2×C4×D4—131no—
356C2×C4×D4—131no—
357C2×C4×D4—131no—
358C22×C4⋊C4—261no—
359#501—138no—
360#501C2×D1318yescomplemented
361#500—138no—
362#479—138no—
363#479—138no—
364#477—138no—
365#476—138no—
366#474—138no—
367#474—138no—
368#446—138no—
369#440—138no—
370#440—138no—
371C4×SD16—138no—
372C2×#107—131no—
373C2×#107—131no—
374C2×#107—131no—
375C2×#107—131no—
376C2×#107C2×D1311yescharacteristic
377C2×#107C2×D1311yescharacteristic
378C2×#106—131no—
379C2×#106C2×D1311yescharacteristic
380C2×#106C2×D1311yescharacteristic
381C2×C4⋊C8—131no—
382C2×C4⋊C8—131no—
383C2×C4⋊C8—131no—
384C2×#103—131no—
385C2×#103—131no—
386C2×#103—131no—
387C2×#102—131no—
388C2×#102—131no—
389C2×#102—131no—
390C2×#97—131no—
391C2×#97C2×D1311yescharacteristic
392C2×C4×C8—131no—
393C22×C13D4×Q812yes—
394C22×C13C2×#13712yes—
395C22×C13#57612yes—
396C22×C13C23×D411yescharacteristic
397C2×D13—24no—
398C2×D13—48no—
399C2×D13—42no—
400C2×D13—42no—
401C4×C13—22no—
402C4×C13—22no—
403C4×C13—42no—
404C4×C13—42no—
405C4×C13—42no—
406C4×C13—42no—
407C4×C13D4×Q812yes—
408C4×C13C23×Q811yescharacteristic
409C4×C13C2×2−1+411yescharacteristic
410Dic13—24no—
411Dic13—22no—
412Dic13—22no—
413Dic13—22no—
414Dic13—42no—
415Dic13—42no—
416Dic13C2×#13714yes—
417C22×Q8—21no—
418C22×Q8—131no—
419C22×Q8—131no—
420C22×Q8—261no—
421C22×Q8—261no—
422C22×Q8—261no—
423C22×D4—131no—
424C23×C4—261no—
425C23×C4—261no—
426C23×C4—261no—
427C2×SD16—138no—
428C2×SD16—134no—
429C22×C8—131no—
430C22×C8—131no—
431C22×C8C22×D1311yescharacteristic
432C22×C8C22×D1311yescharacteristic
433C4⋊Q8—22no—
434C4⋊Q8—134no—
435C4⋊Q8—134no—
436C4⋊Q8—134no—
437C4⋊Q8—262no—
438C4⋊Q8—262no—
439C4⋊Q8—262no—
440C4⋊Q8—268no—
441C4⋊Q8—268no—
442C4⋊Q8—268no—
443C4⋊Q8C22×D1314yes—
444#125—22no—
445#125—134no—
446#125—262no—
447#125C22×D1314yes—
448C22⋊Q8—268no—
449C22⋊Q8—268no—
450C22⋊Q8—268no—
451C4×Q8—134no—
452C4×Q8—134no—
453C4×Q8—134no—
454C4×Q8—134no—
455C4×Q8—134no—
456C4×Q8—262no—
457C4×Q8—262no—
458C4×Q8—268no—
459C4×Q8—262no—
460C4×D4—134no—
461C4×D4—134no—
462C4×D4—134no—
463C4×D4—262no—
464C4×D4—262no—
465C4×D4—262no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—131no—
470C2×C4⋊C4—131no—
471C2×C4⋊C4—131no—
472C2×C4⋊C4—131no—
473C2×C4⋊C4—131no—
474C2×C4⋊C4—268no—
475C2×C4⋊C4—261no—
476C2×C4⋊C4—261no—
477C2×C4⋊C4—261no—
478C2×C4⋊C4—261no—
479C2×C4⋊C4—261no—
480C2×C4⋊C4—261no—
481C2×C4⋊C4—261no—
482C2×C4⋊C4—261no—
483C2×C4⋊C4C22×D1311yescharacteristic
484C2×C4⋊C4C22×D1311yescharacteristic
485C2×C4⋊C4C22×D1311yescharacteristic
486C2×C4⋊C4C22×D1311yescharacteristic
487C2×C22⋊C4—261no—
488C2×C22⋊C4—261no—
489C2×C22⋊C4—261no—
490C2×C42—131no—
491C2×C42—131no—
492C2×C42—261no—
493C2×C42—261no—
494C2×C42—261no—
495C2×C42C22×D1311yescharacteristic
496#107—134no—
497#107—134no—
498#107—134no—
499#107—134no—
500#107C22×D1314yes—
501#107C22×D1314yes—
502#106—134no—
503#106C22×D1314yes—
504#106C22×D1314yes—
505C4⋊C8—134no—
506C4⋊C8—134no—
507C4⋊C8—134no—
508#103—134no—
509#103—134no—
510#103—134no—
511#102—134no—
512#102—134no—
513#102—134no—
514#97—134no—
515#97C22×D1314yes—
516C4×C8—134no—
517C2×C13#338514yescomplemented
518C2×C13C2×D4×Q811yescharacteristic
519C2×C13C22×#13711yescharacteristic
520C2×C13C2×#57611yescharacteristic
521D13—44no—
522C24—261no—
523C2×Q8—24no—
524C2×Q8—82no—
525C2×Q8—134no—
526C2×Q8—134no—
527C2×Q8—132no—
528C2×Q8—264no—
529C2×Q8—264no—
530C2×Q8—264no—
531C2×Q8—264no—
532C2×Q8—261no—
533C2×Q8—262no—
534C2×Q8—1042no—
535C2×Q8—1042no—
536C2×Q8—1042no—
537C2×D4—134no—
538C2×D4—132no—
539C2×D4—261no—
540C2×D4—262no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—131no—
546C22×C4—131no—
547C22×C4—131no—
548C22×C4—131no—
549C22×C4—264no—
550C22×C4—264no—
551C22×C4—261no—
552C22×C4—261no—
553C22×C4—261no—
554C22×C4—264no—
555C22×C4—524no—
556C22×C4—1042no—
557C22×C4—1042no—
558C22×C4D4×D1311yescharacteristic
559C22×C4D4×D1311yescharacteristic
560C22×C4C23×D1311yescharacteristic
561SD16—1316no—
562C2×C8—22no—
563C2×C8—132no—
564C2×C8—132no—
565C2×C8—262no—
566C2×C8—262no—
567C2×C8Q8×D1314yes—
568C2×C8C23×D1312yes—
569C2×C8C23×D1312yes—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—134no—
578C4⋊C4—134no—
579C4⋊C4—134no—
580C4⋊C4—132no—
581C4⋊C4—132no—
582C4⋊C4—264no—
583C4⋊C4—264no—
584C4⋊C4—264no—
585C4⋊C4—264no—
586C4⋊C4—264no—
587C4⋊C4—264no—
588C4⋊C4—264no—
589C4⋊C4—261no—
590C4⋊C4—261no—
591C4⋊C4—264no—
592C4⋊C4C23×D1312yes—
593C4⋊C4C23×D1312yes—
594C4⋊C4C23×D1312yes—
595C4⋊C4C23×D1312yes—
596C22⋊C4—264no—
597C22⋊C4—264no—
598C22⋊C4—264no—
599C42—132no—
600C42—132no—
601C42—132no—
602C42—132no—
603C42—264no—
604C42—264no—
605C42—264no—
606C42D4×D1312yes—
607C42C23×D1312yes—
608C13C2×#338511yescharacteristic, complemented, Sylow
609C23—264no—
610C23—262no—
611C23—522no—
612C23—522no—
613C23C2×D4×D1311yescharacteristic
614Q8—84no—
615Q8—134no—
616Q8—268no—
617Q8—264no—
618Q8—262no—
619Q8—1044no—
620Q8—1044no—
621Q8—1044no—
622D4—134no—
623D4—264no—
624D4—262no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—134no—
636C2×C4—132no—
637C2×C4—132no—
638C2×C4—132no—
639C2×C4—132no—
640C2×C4—264no—
641C2×C4—262no—
642C2×C4—262no—
643C2×C4—262no—
644C2×C4—262no—
645C2×C4—262no—
646C2×C4—262no—
647C2×C4—528no—
648C2×C4—522no—
649C2×C4—522no—
650C2×C4—1044no—
651C2×C4—1044no—
652C2×C4C2×D4×D1312yes—
653C2×C4C2×D4×D1312yes—
654C2×C4C2×D4×D1311yescharacteristic
655C2×C4C2×Q8×D1312yes—
656C2×C4#8825412yes—
657C2×C4C24×D1311yescharacteristic
658C8—22no—
659C8—262no—
660C8—262no—
661C8C2×Q8×D1314yes—
662C22—264no—
663C22—528no—
664C22—522no—
665C22—522no—
666C22#1171943212yes—
667C22#1171947912yes—
668C22D13×#13712yes—
669C22C22×D4×D1311yescharacteristic
670C4—22no—
671C4—22no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4—42no—
676C4—134no—
677C4—262no—
678C4—262no—
679C4—262no—
680C4—264no—
681C4—522no—
682C4—522no—
683C4#1171943212yes—
684C4C22×Q8×D1311yescharacteristic
685C4C2×#8825411yescharacteristic
686C2—524no—
687C2#1312774314yesdirect product factor
688C2C2×#1171943211yescharacteristic
689C2C2×D13×#13711yescharacteristic
690C2C2×#1171947911yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#501C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenterC2×#501D13
hypocenterC13C2×#3385
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#11719427C2semidirect
3. #13127743C2direct (N × H)
4. C2×#11718517C2semidirect
5. C2×#11718535C2semidirect
6. C2×#11718518C2semidirect
7. C2×#11718724C2semidirect
8. C2×#11718536C2semidirect
12. C2×#11718362C2semidirect
16. C2×C13×#501C2semidirect
23. #11719427C22semidirect
43. C13×#501C22semidirect
57. #11718724C22semidirect
69. #11718536C22semidirect
70. #11718535C22semidirect
72. #11718518C22semidirect
73. #11718517C22semidirect
76. #11718362C22semidirect
126. C2×#6095Q8semidirect
263. #6095C2×Q8semidirect
268. C2×#501D13semidirect
360. #501C2×D13semidirect
517. C2×C13#3385semidirect
608. C13C2×#3385semidirect
687. C2#13127743direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117194272
C2×#117193952
#131277432
C2×#117185172
C2×#117185352
C2×#117185182
C2×#117187242
C2×#117185362
C2×#117185312
C2×#117185512
C2×#117187482
C2×#117183622
C2×#117183712
C2×#117185502
C2×#117185132
C2×C13×#5012
C2×#338513