Subgroups — #27136381

Order 12352.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20259996	C₂	1	3	yes	maximal, complemented
2	#20259994	C₂	1	3	yes	maximal, complemented
3	#20259987	C₂	1	1	yes	maximal, characteristic
4	#15690567	C₂²	1	1	yes	characteristic
5	#15690567	C₂²	1	3	yes	—
6	#15690565	C₄	1	3	yes	—
7	#15690563	C₂²	1	3	yes	—
8	#15690556	C₄	1	1	yes	characteristic
9	#13095400	C₂×C₄	1	3	yes	—
10	#13095400	C₂³	1	1	yes	characteristic
11	D₇₇₂	C₈	1	3	yes	—
12	C₄×D₁₉₃	C₂×C₄	1	3	yes	—
13	Q₈×C₁₉₃	C₈	1	1	yes	characteristic
14	C₂×D₁₉₃	C₂×C₈	1	3	yes	—
15	C₄×C₁₉₃	C₂×C₈	1	3	yes	—
16	Dic₁₉₃	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₁₉₃	C₂²×C₈	1	1	yes	characteristic
18	D₁₉₃	—	2	3	no	—
19	C₁₉₃	#504	1	1	yes	characteristic, complemented, Sylow
20	#504	—	193	1	no	maximal, Sylow
21	#131	—	193	1	no	—
22	M₃₂	—	193	3	no	—
23	C₂×C₁₆	—	193	3	no	—
24	#41	—	193	1	no	—
25	M₁₆	—	193	3	no	—
26	C₂×C₈	—	193	3	no	—
27	C₁₆	—	193	1	no	—
28	C₁₆	—	193	3	no	—
29	Q₈	#13095402	1	1	yes	characteristic
30	D₄	—	193	3	no	—
31	C₂×C₄	—	193	3	no	—
32	C₈	—	193	1	no	—
33	C₈	—	193	3	no	—
34	C₂²	—	193	3	no	—
35	C₄	—	193	1	no	—
36	C₄	C₂×#13095402	1	3	yes	—
37	C₂	—	386	3	no	—
38	C₂	C₂²×#13095402	1	1	yes	characteristic

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

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