Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
369 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 369 conjugacy classes of subgroups — too many to draw. Only its 122 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. C32×#500 | C2 | semidirect |
| 3. C3×#4491 | C2 | semidirect |
| 4. C3×C4×C3⋊C16 | C2 | semidirect |
| 6. #71381 | C3 | direct (N × H) |
| 16. C3×#500 | D3 | semidirect |
| 17. C3×#500 | C2×C3 | semidirect |
| 22. #4491 | C2×C3 | semidirect |
| 23. C4×C3⋊C16 | C2×C3 | semidirect |
| 69. #500 | C3×D3 | semidirect |
| 191. C32 | #2240 | semidirect |
| 225. C3 | #71381 | direct (N × H) |
| 226. C3 | C3×#2240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#500 | 2 |
| C3×#4695 | 2 |
| C3×#4491 | 2 |
| C3×C4×C3⋊C16 | 2 |
| C3×#2240 | 3 |
| #71381 | 3 |