Subgroups — #36346004

Order 21856.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₃₆₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₂₇₃₂	C₂	1	1	yes	maximal, characteristic
3	(C₂×D₆₈₃)⋊C₄	C₂	1	4	yes	maximal, complemented
4	C₄²×C₆₈₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₆₈₃	C₂²	1	2	yes	—
6	Dic₁₃₆₆	—	2	2	no	—
7	D₂₇₃₂	—	2	2	no	—
8	C₂×Dic₆₈₃	C₂²	1	2	yes	—
9	C₂×C₄×C₆₈₃	C₂²	1	2	yes	—
10	C₂×C₄×C₆₈₃	C₂²	1	1	yes	characteristic
11	C₂²×C₆₈₃	C₂³	1	1	yes	characteristic
12	C₂×D₆₈₃	—	2	2	no	—
13	C₂×D₆₈₃	—	2	4	no	—
14	C₄×C₆₈₃	—	2	2	no	—
15	C₄×C₆₈₃	D₄	1	2	yes	—
16	Dic₆₈₃	—	2	2	no	—
17	C₂×C₆₈₃	C₂×D₄	1	1	yes	characteristic
18	C₂×C₆₈₃	#41	1	2	yes	—
19	D₆₈₃	—	4	2	no	—
20	C₆₈₃	#124	1	1	yes	characteristic, complemented, Sylow
21	#124	—	683	1	no	maximal, Sylow
22	C₂×Q₈	—	683	1	no	—
23	C₂×D₄	—	683	1	no	—
24	C₂²⋊C₄	—	683	4	no	—
25	C₄²	D₆₈₃	1	1	yes	characteristic, complemented
26	C₂³	—	683	2	no	—
27	Q₈	—	1366	2	no	—
28	D₄	—	1366	2	no	—
29	C₂×C₄	—	683	2	no	—
30	C₂×C₄	C₂×D₆₈₃	1	2	yes	—
31	C₂×C₄	C₂×D₆₈₃	1	1	yes	characteristic
32	C₂²	—	1366	2	no	—
33	C₂²	—	1366	4	no	—
34	C₂²	C₂²×D₆₈₃	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	1366	2	no	—
37	C₄	D₂₇₃₂	1	2	yes	—
38	C₂	—	2732	2	no	—
39	C₂	C₂×D₂₇₃₂	1	1	yes	characteristic
40	C₂	#24926421	1	2	yes	—

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.