Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
405 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 405 conjugacy classes of subgroups — too many to draw. Only its 100 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. #10592380 | C2 | semidirect |
| 3. #10590288 | C2 | semidirect |
| 4. #10590287 | C2 | semidirect |
| 7. C3×C8×C3⋊C8 | C2 | semidirect |
| 37. C8×C3⋊C8 | D3 | semidirect |
| 257. C32 | #1711 | semidirect |
| 296. C3 | #68061 | semidirect |
| 297. C3 | #71183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592380 | 2 |
| C3×#4694 | 2 |
| #10590288 | 2 |
| #10590287 | 2 |
| #10590273 | 2 |
| C3×C8×C3⋊C8 | 2 |
| #71183 | 3 |
| #68061 | 3 |