Subgroups — C₂×Q₈×C₉ #3706

Order 144.

57 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₉	C₂	1	4	yes	maximal, direct product factor
2	C₂×C₄×C₉	C₂	1	3	yes	maximal
3	C₂×C₃×Q₈	C₃	1	1	yes	maximal, characteristic
4	C₂²×C₉	C₂²	1	1	yes	characteristic
5	C₄×C₉	C₂²	1	6	yes	—
6	C₃×Q₈	C₂×C₃	1	4	yes	—
7	C₂×C₃×C₄	C₂×C₃	1	3	yes	—
8	C₂×C₉	Q₈	1	2	yes	direct product factor
9	C₂×C₉	C₂³	1	1	yes	characteristic
10	C₂×Q₈	C₉	1	1	yes	characteristic, direct product factor, Sylow
11	C₂²×C₃	C₂²×C₃	1	1	yes	characteristic
12	C₃×C₄	C₂²×C₃	1	6	yes	—
13	C₉	C₂×Q₈	1	1	yes	characteristic, direct product factor, Sylow
14	Q₈	C₂×C₉	1	4	yes	direct product factor
15	C₂×C₄	C₂×C₉	1	3	yes	—
16	C₂×C₃	C₃×Q₈	1	2	yes	—
17	C₂×C₃	C₂³×C₃	1	1	yes	characteristic
18	C₂²	C₂²×C₉	1	1	yes	characteristic
19	C₄	C₂²×C₉	1	6	yes	—
20	C₃	C₂×C₃×Q₈	1	1	yes	characteristic
21	C₂	Q₈×C₉	1	2	yes	direct product factor
22	C₂	C₂³×C₉	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.