Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1080 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 261 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. C32×#499 | C2 | semidirect |
| 3. #10592764 | C2 | semidirect |
| 5. #10592577 | C2 | semidirect |
| 7. #10592557 | C2 | semidirect |
| 9. #10592382 | C2 | semidirect |
| 31. C3×#499 | D3 | semidirect |
| 98. #499 | C3⋊D3 | direct (N × H) |
| 167. C3⋊D3 | #499 | direct (N × H) |
| 197. C32 | C2×#499 | semidirect |
| 226. C3 | D3×#499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×#125 | 2 |
| C32×#499 | 2 |
| #10592764 | 2 |
| C3⋊D3×#107 | 2 |
| #10592577 | 2 |
| C3⋊D3×#106 | 2 |
| #10592557 | 2 |
| C4×C8×C3⋊D3 | 2 |
| #10592382 | 2 |
| D3×#499 | 3 |