Subgroups — #826

Order 96.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₆	—	3	1	no	maximal, Sylow
5	C₃×D₄	—	2	1	no	—
6	D₁₂	—	2	1	no	—
7	C₃×C₈	C₂²	1	1	yes	characteristic
8	D₈	—	3	1	no	—
9	D₈	D₃	1	1	yes	characteristic, complemented
10	C₁₆	—	3	1	no	—
11	C₂²×C₃	—	4	1	no	—
12	C₂×D₃	—	4	1	no	—
13	C₃×C₄	D₄	1	1	yes	characteristic
14	D₄	—	2	1	no	—
15	D₄	—	6	1	no	—
16	C₈	C₂×D₃	1	1	yes	characteristic
17	C₂×C₃	—	8	1	no	—
18	C₂×C₃	D₈	1	1	yes	characteristic
19	D₃	—	8	1	no	—
20	C₂²	—	4	1	no	—
21	C₂²	—	12	1	no	—
22	C₄	#67	1	1	yes	characteristic
23	C₃	D₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₂	—	8	1	no	—
25	C₂	—	24	1	no	—
26	C₂	#213	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.