Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
327 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 327 conjugacy classes of subgroups — too many to draw. Only its 72 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×#4907 | C2 | semidirect |
| 2. #10590927 | C2 | semidirect |
| 3. #10590926 | C2 | semidirect |
| 4. C2×#63546 | C2 | semidirect |
| 5. #10589382 | C2 | semidirect |
| 6. C3×#4516 | C2 | semidirect |
| 7. #10589143 | C2 | semidirect |
| 30. #4907 | D3 | semidirect |
| 37. #4516 | D3 | semidirect |
| 274. C32 | #2221 | semidirect |
| 314. C3 | #69260 | semidirect |
| 315. C3 | #71454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4907 | 2 |
| #10590927 | 2 |
| #10590926 | 2 |
| C2×#63546 | 2 |
| #10589382 | 2 |
| C3×#4516 | 2 |
| #10589143 | 2 |
| #71454 | 3 |
| #69260 | 3 |