Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
307 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 307 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 |
|---|---|---|
| 2. C3×#4716 | C2 | semidirect |
| 4. #10589332 | C2 | semidirect |
| 5. #10589138 | C2 | semidirect |
| 6. #10589129 | C2 | semidirect |
| 21. #63550 | C4 | semidirect |
| 22. #63547 | C4 | semidirect |
| 28. #4716 | D3 | semidirect |
| 243. C32 | #2180 | semidirect |
| 275. C3 | #70917 | semidirect |
| 276. C3 | #70928 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4717 | 2 |
| C3×#4716 | 2 |
| #10590636 | 2 |
| #10589332 | 2 |
| #10589138 | 2 |
| #10589129 | 2 |
| #10589123 | 2 |
| #70928 | 3 |
| #70917 | 3 |