Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
269 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 269 conjugacy classes of subgroups — too many to draw. Only its 70 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. #10590871 | C2 | semidirect |
| 4. C3×#4513 | C2 | semidirect |
| 5. C3×#4511 | C2 | semidirect |
| 6. #10589137 | C2 | semidirect |
| 32. #4513 | D3 | semidirect |
| 33. #4511 | D3 | semidirect |
| 231. C32 | #2231 | semidirect |
| 263. C3 | #69308 | semidirect |
| 264. C3 | #69316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590917 | 2 |
| #10590871 | 2 |
| #10589384 | 2 |
| C3×#4513 | 2 |
| C3×#4511 | 2 |
| #10589137 | 2 |
| #10589125 | 2 |
| #69316 | 3 |
| #69308 | 3 |