Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
684 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 143 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×#477 | C2 | semidirect |
| 4. #10592778 | C2 | semidirect |
| 5. #10589401 | C2 | semidirect |
| 7. #10589348 | C2 | semidirect |
| 27. C3×#477 | D3 | semidirect |
| 100. #477 | C3⋊D3 | semidirect |
| 225. C32 | #1637 | semidirect |
| 267. C3 | #71163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C4⋊(C3⋊D3) | 2 |
| C32×#477 | 2 |
| #10592783 | 2 |
| #10592778 | 2 |
| #10589401 | 2 |
| #10589349 | 2 |
| #10589348 | 2 |
| #71163 | 3 |