Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
391 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 391 conjugacy classes of subgroups — too many to draw. Only its 96 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×#4693 | C2 | semidirect |
| 2. C3×#4688 | C2 | semidirect |
| 4. #10590269 | C2 | semidirect |
| 5. #10589324 | C2 | semidirect |
| 6. #10589093 | C2 | semidirect |
| 7. #10589090 | C2 | semidirect |
| 31. #4693 | D3 | semidirect |
| 32. #4688 | D3 | semidirect |
| 113. C32×C8 | D8 | semidirect |
| 242. C3×C8 | #213 | semidirect |
| 243. C3×C8 | #213 | semidirect |
| 310. C32 | #1685 | semidirect |
| 333. C8 | #3713 | semidirect |
| 362. C3 | #70867 | semidirect |
| 363. C3 | #71268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4693 | 2 |
| C3×#4688 | 2 |
| #10590347 | 2 |
| #10590269 | 2 |
| #10589324 | 2 |
| #10589093 | 2 |
| #10589090 | 2 |
| #71268 | 3 |
| #70867 | 3 |