Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
327 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 327 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 4. #10589355 | C2 | semidirect |
| 5. C3×#4490 | C2 | semidirect |
| 6. #10589141 | C2 | semidirect |
| 7. #10589140 | C2 | semidirect |
| 21. D3×C3⋊C16 | C4 | semidirect |
| 31. #4490 | D3 | semidirect |
| 231. C32 | #2158 | semidirect |
| 267. C3 | #69345 | semidirect |
| 268. C3 | #70648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4880 | 2 |
| #10590707 | 2 |
| C2×D3×C3⋊C16 | 2 |
| #10589355 | 2 |
| C3×#4490 | 2 |
| #10589141 | 2 |
| #10589140 | 2 |
| #70648 | 3 |
| #69345 | 3 |