Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
353 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 353 conjugacy classes of subgroups — too many to draw. Only its 88 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. C3×#4874 | C2 | semidirect |
| 3. #10589357 | C2 | semidirect |
| 4. C3×#4491 | C2 | semidirect |
| 5. #10589116 | C2 | semidirect |
| 6. #10589114 | C2 | semidirect |
| 7. Dic3×C3⋊C16 | C2 | semidirect |
| 23. #4874 | D3 | semidirect |
| 34. #4491 | D3 | semidirect |
| 267. C32 | #2240 | semidirect |
| 313. C3 | #69183 | semidirect |
| 314. C3 | #71381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4874 | 2 |
| #10590880 | 2 |
| #10589357 | 2 |
| C3×#4491 | 2 |
| #10589116 | 2 |
| #10589114 | 2 |
| Dic3×C3⋊C16 | 2 |
| #71381 | 3 |
| #69183 | 3 |