Subgroups — #27135081

Order 12352.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20259839	C₂	1	1	yes	maximal, characteristic
2	#20259835	C₂	1	1	yes	maximal, characteristic
3	#106×C₁₉₃	C₂	1	1	yes	maximal, characteristic
4	#15690539	—	2	1	no	—
5	#15690530	C₄	1	2	yes	complemented
6	C₂×C₈×C₁₉₃	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₁₉₃	—	2	1	no	—
8	#13095393	—	4	1	no	—
9	C₂×C₄×C₁₉₃	—	4	1	no	—
10	C₂×C₄×C₁₉₃	D₄	1	1	yes	characteristic
11	C₈×C₁₉₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₉₃	Q₈	1	1	yes	characteristic
13	C₂²×C₁₉₃	SD₁₆	1	1	yes	characteristic
14	C₄×C₁₉₃	—	8	1	no	—
15	C₄×C₁₉₃	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₁₉₃	SD₁₆	1	1	yes	characteristic
17	C₂×C₁₉₃	—	2	1	no	—
18	C₂×C₁₉₃	#106	1	1	yes	characteristic
19	C₁₉₃	#365	1	1	yes	characteristic, complemented, Sylow
20	#365	—	193	1	no	maximal, Sylow
21	M₃₂	—	193	1	no	—
22	#108	—	193	1	no	—
23	#106	D₁₉₃	1	1	yes	characteristic
24	M₁₆	—	386	1	no	—
25	C₂×C₈	C₂×D₁₉₃	1	1	yes	characteristic
26	C₄⋊C₄	—	2	1	no	—
27	C₁₆	—	193	2	no	—
28	C₂×C₄	—	4	1	no	—
29	C₂×C₄	C₂²⋊D₁₉₃	1	1	yes	characteristic
30	C₈	—	772	1	no	—
31	C₈	C₄×D₁₉₃	1	1	yes	characteristic
32	C₈	Dic₃₈₆	1	1	yes	characteristic
33	C₂²	#15690543	1	1	yes	characteristic
34	C₄	—	8	1	no	—
35	C₄	#15690534	1	1	yes	characteristic
36	C₄	#15690542	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#20259830	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. #15690530	C₄	semidirect
19. C₁₉₃	#365	semidirect

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