Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
451 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 451 conjugacy classes of subgroups — too many to draw. Only its 116 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. C3×#4680 | C2 | semidirect |
| 3. #10590287 | C2 | semidirect |
| 5. C3×C8×C3⋊C8 | C2 | semidirect |
| 25. #4680 | D3 | semidirect |
| 27. C8×C3⋊C8 | D3 | semidirect |
| 187. C32 | #1708 | semidirect |
| 216. C3 | #68059 | semidirect |
| 217. C3 | #71334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592392 | 2 |
| C3×#4680 | 2 |
| #10590287 | 2 |
| #10590281 | 2 |
| C3×C8×C3⋊C8 | 2 |
| #71334 | 3 |
| #68059 | 3 |