Subgroups — C₂²×Dic₁₈ #63704

Order 288.

234 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₉	C₂	1	2	yes	maximal
3	C₂×Dic₁₈	C₂	1	12	yes	maximal, direct product factor
4	C₂²×Dic₆	—	3	1	no	maximal
5	C₂³×C₉	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₉	C₂²	1	6	yes	—
7	C₂×Dic₉	C₂²	1	12	yes	—
8	Dic₁₈	C₂²	1	16	yes	direct product factor
9	C₂²×C₃×C₄	D₃	1	1	yes	characteristic
10	C₂²×Dic₃	—	3	2	no	—
11	C₂×Dic₆	—	3	12	no	—
12	C₂²×C₉	Q₈	1	4	yes	complemented
13	C₂²×C₉	C₂³	1	3	yes	—
14	C₄×C₉	C₂³	1	4	yes	—
15	Dic₉	C₂³	1	8	yes	—
16	C₂²×Q₈	—	9	1	no	Sylow
17	C₂³×C₃	C₂×D₃	1	1	yes	characteristic
18	C₂×C₃×C₄	C₂×D₃	1	6	yes	—
19	C₂×Dic₃	—	3	12	no	—
20	Dic₆	—	3	16	no	—
21	C₂×C₉	C₂×Q₈	1	6	yes	complemented
22	C₂×C₉	C₂⁴	1	1	yes	characteristic
23	C₂×Q₈	—	9	12	no	—
24	C₂²×C₄	—	9	2	no	—
25	C₂²×C₄	D₉	1	1	yes	characteristic
26	C₂²×C₃	Dic₆	1	4	yes	—
27	C₂²×C₃	C₂²×D₃	1	3	yes	—
28	C₃×C₄	C₂²×D₃	1	4	yes	—
29	Dic₃	—	3	8	no	—
30	C₉	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
31	C₂³	C₂×D₉	1	1	yes	characteristic
32	Q₈	—	9	16	no	—
33	C₂×C₄	—	9	12	no	—
34	C₂×C₄	C₂×D₉	1	6	yes	—
35	C₂×C₃	C₂×Dic₆	1	6	yes	—
36	C₂×C₃	C₂³×D₃	1	1	yes	characteristic
37	C₂²	Dic₁₈	1	4	yes	direct product factor
38	C₂²	C₂²×D₉	1	3	yes	—
39	C₄	—	9	8	no	—
40	C₄	C₂²×D₉	1	4	yes	—
41	C₃	C₂²×Dic₆	1	1	yes	characteristic
42	C₂	C₂×Dic₁₈	1	6	yes	direct product factor
43	C₂	C₂³×D₉	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.