Subgroups — C₃²×#100 #63670

Order 288.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×D₄	C₂	1	1	yes	maximal, characteristic
2	C₃²×M₁₆	C₂	1	2	yes	maximal, complemented
3	C₃×#100	C₃	1	4	yes	maximal, direct product factor
4	C₂³×C₃²	C₄	1	2	yes	—
5	C₃²×D₄	—	2	2	no	—
6	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
7	C₃²×C₈	—	2	2	no	—
8	C₂×C₃×D₄	C₂×C₃	1	4	yes	—
9	C₃×M₁₆	C₂×C₃	1	8	yes	complemented
10	C₂²×C₃²	—	2	2	no	—
11	C₂²×C₃²	—	4	2	no	—
12	C₂²×C₃²	C₂×C₄	1	1	yes	characteristic
13	C₃²×C₄	D₄	1	2	yes	—
14	#100	C₃²	1	1	yes	characteristic, direct product factor, Sylow
15	C₂³×C₃	C₃×C₄	1	8	yes	—
16	C₃×D₄	—	2	8	no	—
17	C₂×C₃×C₄	C₂²×C₃	1	4	yes	—
18	C₃×C₈	—	2	8	no	—
19	C₂×C₃²	—	2	1	no	—
20	C₂×C₃²	—	4	2	no	—
21	C₂×C₃²	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×D₄	C₂×C₃²	1	1	yes	characteristic
23	M₁₆	C₂×C₃²	1	2	yes	complemented
24	C₂²×C₃	—	2	8	no	—
25	C₂²×C₃	—	4	8	no	—
26	C₂²×C₃	C₂×C₃×C₄	1	4	yes	—
27	C₃×C₄	C₃×D₄	1	8	yes	—
28	C₃²	#100	1	1	yes	characteristic, direct product factor, Sylow
29	C₂³	C₃²×C₄	1	2	yes	—
30	D₄	—	2	2	no	—
31	C₂×C₄	C₂²×C₃²	1	1	yes	characteristic
32	C₈	—	2	2	no	—
33	C₂×C₃	—	2	4	no	—
34	C₂×C₃	—	4	8	no	—
35	C₂×C₃	C₃×C₂²⋊C₄	1	4	yes	—
36	C₂²	—	2	2	no	—
37	C₂²	—	4	2	no	—
38	C₂²	C₂×C₃²×C₄	1	1	yes	characteristic
39	C₄	C₃²×D₄	1	2	yes	—
40	C₃	C₃×#100	1	4	yes	direct product factor
41	C₂	—	2	1	no	—
42	C₂	—	4	2	no	—
43	C₂	C₃²×C₂²⋊C₄	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.