Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
321 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 321 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
| 4. C3×#4565 | C2 | semidirect |
| 5. C3×#4506 | C2 | semidirect |
| 7. #71507 | C3 | direct (N × H) |
| 20. C2×C3×Q32 | D3 | semidirect |
| 21. C2×C3×Q32 | C2×C3 | semidirect |
| 28. #4565 | C2×C3 | semidirect |
| 29. #4506 | C2×C3 | semidirect |
| 83. C2×Q32 | C3×D3 | semidirect |
| 202. C32 | #2222 | semidirect |
| 230. C3 | #71507 | direct (N × H) |
| 231. C3 | C3×#2222 | 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×#5192 | 2 |
| C3×#4901 | 2 |
| C3×#4565 | 2 |
| C3×#4506 | 2 |
| C3×#2222 | 3 |
| #71507 | 3 |