Subgroups — #36346003

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	C₂²⋊Dic₆₈₃	C₂	1	4	yes	maximal, complemented
3	C₄×Dic₆₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×C₆₈₃	C₂	1	1	yes	maximal, characteristic
5	Dic₁₃₆₆	—	2	2	no	—
6	C₂×Dic₆₈₃	C₂²	1	2	yes	—
7	C₂×Dic₆₈₃	C₂²	1	2	yes	—
8	C₂³×C₆₈₃	C₂²	1	2	yes	—
9	D₄×C₆₈₃	—	2	2	no	—
10	C₂×C₄×C₆₈₃	C₂²	1	1	yes	characteristic
11	C₂²×C₆₈₃	—	2	2	no	—
12	C₂²×C₆₈₃	—	2	4	no	—
13	C₂²×C₆₈₃	C₂³	1	1	yes	characteristic
14	C₄×C₆₈₃	D₄	1	2	yes	—
15	Dic₆₈₃	—	2	2	no	—
16	Dic₆₈₃	—	2	2	no	—
17	C₂×C₆₈₃	—	4	2	no	—
18	C₂×C₆₈₃	C₂×D₄	1	1	yes	characteristic
19	C₂×C₆₈₃	#41	1	2	yes	—
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	D₆₈₃	1	1	yes	characteristic
24	C₂²⋊C₄	—	683	4	no	—
25	C₄²	—	683	1	no	—
26	C₂³	C₂×D₆₈₃	1	2	yes	—
27	Q₈	—	1366	2	no	—
28	D₄	—	2	2	no	—
29	C₂×C₄	—	683	2	no	—
30	C₂×C₄	—	683	2	no	—
31	C₂×C₄	C₂×D₆₈₃	1	1	yes	characteristic
32	C₂²	—	2	2	no	—
33	C₂²	—	2	4	no	—
34	C₂²	C₂²×D₆₈₃	1	1	yes	characteristic
35	C₄	—	1366	2	no	—
36	C₄	—	1366	2	no	—
37	C₄	C₂²⋊D₆₈₃	1	2	yes	—
38	C₂	—	4	2	no	—
39	C₂	C₂×C₂²⋊D₆₈₃	1	1	yes	characteristic
40	C₂	#24926420	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.