Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
297 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 297 conjugacy classes of subgroups — too many to draw. Only its 76 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. #10590875 | C2 | semidirect |
| 3. #10589367 | C2 | semidirect |
| 5. C3×#4504 | C2 | semidirect |
| 6. #10589142 | C2 | semidirect |
| 29. #4504 | D3 | semidirect |
| 232. C32 | #2228 | semidirect |
| 269. C3 | #69180 | semidirect |
| 270. C3 | #69334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590875 | 2 |
| #10590777 | 2 |
| #10589367 | 2 |
| C3×#4509 | 2 |
| C3×#4504 | 2 |
| #10589142 | 2 |
| #10589114 | 2 |
| #69334 | 3 |
| #69180 | 3 |