Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
927 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 927 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×#407 | C2 | semidirect |
| 3. C4×#3676 | C2 | semidirect |
| 4. C2×#63384 | C2 | semidirect |
| 11. C2×#3697 | C4 | semidirect |
| 13. C22×D36 | C4 | semidirect |
| 15. C22×Dic18 | C4 | semidirect |
| 16. C2×C9×M16 | C22 | semidirect |
| 18. C2×C4×Dic9 | C22 | semidirect |
| 107. D36 | C22⋊C4 | semidirect |
| 112. Dic18 | C22⋊C4 | semidirect |
| 116. #407 | D9 | semidirect |
| 159. C22×C9 | #104 | semidirect |
| 182. C2×M16 | C2×D9 | semidirect |
| 286. C9 | #1789 | semidirect |
| 342. C22 | #63384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3697 | 2 |
| C9×#407 | 2 |
| C4×#3676 | 2 |
| C2×#63384 | 2 |
| #69991 | 3 |