Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
456 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 1. C32×#499 | C2 | semidirect |
| 3. #10589357 | C2 | semidirect |
| 4. #10589327 | C2 | semidirect |
| 14. C3×#499 | D3 | semidirect |
| 46. #499 | C3⋊D3 | semidirect |
| 104. C32 | #2244 | semidirect |
| 124. C3 | #71352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#499 | 2 |
| #10592394 | 2 |
| #10589357 | 2 |
| #10589327 | 2 |
| #71352 | 3 |