Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 4. #10592380 | C2 | semidirect |
| 5. C32×#334 | C2 | semidirect |
| 6. #10589352 | C2 | semidirect |
| 7. #10589348 | C2 | semidirect |
| 28. C3×#334 | D3 | semidirect |
| 89. #334 | C3⋊D3 | semidirect |
| 191. C32 | #1679 | semidirect |
| 228. C3 | #68539 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592545 | 2 |
| #10592540 | 2 |
| C8×C4⋊(C3⋊D3) | 2 |
| #10592380 | 2 |
| C32×#334 | 2 |
| #10589352 | 2 |
| #10589348 | 2 |
| #68539 | 3 |