Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1265 conjugacy classes of subgroups; only the 252 normal subgroups are shown.
This group has 1265 conjugacy classes of subgroups — too many to draw. Only its 252 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 |
|---|---|---|
| 1. C22×C3×#204 | C2 | semidirect |
| 2. C2×#63863 | C2 | semidirect |
| 3. C22×#3718 | C2 | semidirect |
| 5. C2×C8×C3⋊Dic3 | C2 | semidirect |
| 6. #10590867 | C2 | direct (N × H) |
| 14. C2×C3×#204 | C22 | semidirect |
| 17. #63863 | C22 | semidirect |
| 19. C2×#3718 | C22 | semidirect |
| 22. C8×C3⋊Dic3 | C22 | semidirect |
| 28. C22×#204 | D3 | semidirect |
| 78. C2×#204 | C2×D3 | semidirect |
| 215. C2×C32 | #495 | semidirect |
| 263. C32 | C2×#495 | semidirect |
| 288. C2×C3 | #5168 | semidirect |
| 304. C3 | C2×#5168 | semidirect |
| 306. C2 | #10590867 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#204 | 2 |
| C2×#63863 | 2 |
| C22×#3718 | 2 |
| C22×#3713 | 2 |
| C2×C8×C3⋊Dic3 | 2 |
| #10590867 | 2 |
| C2×#5168 | 3 |