Subgroups — #27133838

Order 12256.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₅₃₂	C₂	1	6	yes	maximal, complemented
2	C₄²×C₃₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₃₈₃	C₂²	1	4	yes	—
4	D₁₅₃₂	—	2	12	no	—
5	C₂×C₄×C₃₈₃	C₂²	1	3	yes	—
6	C₂²×C₃₈₃	C₂³	1	1	yes	characteristic
7	C₂×D₃₈₃	—	2	12	no	—
8	C₄×C₃₈₃	D₄	1	6	yes	complemented
9	C₂×C₃₈₃	C₂×D₄	1	3	yes	—
10	D₃₈₃	—	4	4	no	—
11	C₃₈₃	#127	1	1	yes	characteristic, complemented, Sylow
12	#127	—	383	1	no	maximal, Sylow
13	C₂×D₄	—	383	6	no	—
14	C₄²	D₃₈₃	1	1	yes	characteristic, complemented
15	C₂³	—	383	4	no	—
16	D₄	—	766	12	no	—
17	C₂×C₄	C₂×D₃₈₃	1	3	yes	—
18	C₂²	—	766	12	no	—
19	C₂²	C₂²×D₃₈₃	1	1	yes	characteristic
20	C₄	D₁₅₃₂	1	6	yes	complemented
21	C₂	—	1532	4	no	—
22	C₂	C₂×D₁₅₃₂	1	3	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.