Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
316 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 92 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. #10590624 | C2 | semidirect |
| 3. #10590621 | C2 | semidirect |
| 4. #10589374 | C2 | semidirect |
| 5. C3×#4508 | C2 | semidirect |
| 6. C3×#4502 | C2 | semidirect |
| 7. #10589134 | C2 | semidirect |
| 37. #4508 | D3 | semidirect |
| 38. #4502 | D3 | semidirect |
| 272. C32 | #2171 | semidirect |
| 309. C3 | #69076 | semidirect |
| 310. C3 | #69123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590923 | 2 |
| #10590624 | 2 |
| #10590621 | 2 |
| #10589374 | 2 |
| C3×#4508 | 2 |
| C3×#4502 | 2 |
| #10589134 | 2 |
| #69123 | 3 |
| #69076 | 3 |