Subgroups — D₁₉₂ #67433

Order 384.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉₆	C₂	1	2	yes	maximal, complemented
2	C₃×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	D₆₄	—	3	1	no	maximal, Sylow
4	D₄₈	—	2	2	no	—
5	C₃×C₃₂	C₂²	1	1	yes	characteristic
6	D₃₂	—	3	2	no	—
7	C₆₄	D₃	1	1	yes	characteristic, complemented
8	D₂₄	—	4	2	no	—
9	C₃×C₁₆	D₄	1	1	yes	characteristic
10	D₁₆	—	6	2	no	—
11	C₃₂	C₂×D₃	1	1	yes	characteristic
12	D₁₂	—	8	2	no	—
13	C₃×C₈	D₈	1	1	yes	characteristic
14	D₈	—	12	2	no	—
15	C₁₆	D₁₂	1	1	yes	characteristic
16	C₂×D₃	—	16	2	no	—
17	C₃×C₄	D₁₆	1	1	yes	characteristic
18	D₄	—	24	2	no	—
19	C₈	D₂₄	1	1	yes	characteristic
20	C₂×C₃	D₃₂	1	1	yes	characteristic
21	D₃	—	32	2	no	—
22	C₂²	—	48	2	no	—
23	C₄	D₄₈	1	1	yes	characteristic
24	C₃	D₆₄	1	1	yes	characteristic, complemented, Sylow
25	C₂	—	96	2	no	—
26	C₂	D₉₆	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.