Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
249 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 249 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×C32×Q32 | C2 | semidirect |
| 3. C3×#4522 | C2 | semidirect |
| 4. C3×#4521 | C2 | semidirect |
| 5. C3×#4499 | C2 | semidirect |
| 7. #71493 | C3 | direct (N × H) |
| 19. C2×C3×Q32 | D3 | semidirect |
| 20. C2×C3×Q32 | C2×C3 | semidirect |
| 25. #4522 | C2×C3 | semidirect |
| 26. #4521 | C2×C3 | semidirect |
| 27. #4499 | C2×C3 | semidirect |
| 72. C2×Q32 | C3×D3 | semidirect |
| 172. C32 | #2264 | semidirect |
| 198. C3 | #71493 | direct (N × H) |
| 199. C3 | C3×#2264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q32 | 2 |
| C3×#4904 | 2 |
| C3×#4522 | 2 |
| C3×#4521 | 2 |
| C3×#4499 | 2 |
| C3×#2264 | 3 |
| #71493 | 3 |