Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
793 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 793 conjugacy classes of subgroups — too many to draw. Only its 188 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 |
|---|---|---|
| 3. C3×#4683 | C2 | semidirect |
| 4. #10590902 | C2 | semidirect |
| 5. #10590900 | C2 | semidirect |
| 8. #10590314 | C2 | semidirect |
| 35. #4683 | D3 | semidirect |
| 46. C8×C3⋊D3 | Q8 | semidirect |
| 47. C8×C3⋊D3 | Q8 | semidirect |
| 222. C32 | #3160 | semidirect |
| 253. C3 | #81916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593854 | 2 |
| C4×C8×C3⋊D3 | 2 |
| C3×#4683 | 2 |
| #10590902 | 2 |
| #10590900 | 2 |
| #10590714 | 2 |
| #10590712 | 2 |
| #10590314 | 2 |
| #81916 | 3 |