Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
516 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 141 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. #10592381 | C2 | semidirect |
| 4. C32×#335 | C2 | semidirect |
| 5. #10589348 | C2 | semidirect |
| 21. C3×#335 | D3 | semidirect |
| 63. C32×C8 | SD16 | semidirect |
| 68. #335 | C3⋊D3 | semidirect |
| 120. C3×C8 | #204 | semidirect |
| 151. C32 | #1673 | semidirect |
| 167. C8 | #3744 | semidirect |
| 183. C3 | #68578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592540 | 2 |
| C8×C4⋊(C3⋊D3) | 2 |
| #10592381 | 2 |
| C32×#335 | 2 |
| #10589348 | 2 |
| #68578 | 3 |