Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
391 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 391 conjugacy classes of subgroups — too many to draw. Only its 84 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. #10590375 | C2 | semidirect |
| 3. #10590339 | C2 | semidirect |
| 4. #10590269 | C2 | semidirect |
| 5. #10589345 | C2 | semidirect |
| 6. C3×#4486 | C2 | semidirect |
| 7. #10589090 | C2 | semidirect |
| 35. #4486 | D3 | semidirect |
| 115. C3⋊(C3⋊C8) | D8 | semidirect |
| 310. C32 | #1685 | semidirect |
| 362. C3 | #68448 | semidirect |
| 363. C3 | #71008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4843 | 2 |
| #10590375 | 2 |
| #10590339 | 2 |
| #10590269 | 2 |
| #10589345 | 2 |
| C3×#4486 | 2 |
| #10589090 | 2 |
| #71008 | 3 |
| #68448 | 3 |