Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
364 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 88 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×#4830 | C2 | semidirect |
| 2. #10590385 | C2 | semidirect |
| 5. #10589352 | C2 | semidirect |
| 7. #10589099 | C2 | semidirect |
| 31. #4830 | D3 | semidirect |
| 292. C32 | #1682 | semidirect |
| 338. C3 | #68411 | semidirect |
| 339. C3 | #70941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4830 | 2 |
| #10590385 | 2 |
| #10590364 | 2 |
| #10590273 | 2 |
| #10589352 | 2 |
| C3×#4485 | 2 |
| #10589099 | 2 |
| #70941 | 3 |
| #68411 | 3 |