Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
742 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 196 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. C3×#5753 | C2 | semidirect |
| 2. #10592839 | C2 | semidirect |
| 3. C2×#63550 | C2 | semidirect |
| 4. #10590636 | C2 | semidirect |
| 5. #10590629 | C2 | semidirect |
| 19. #5753 | D3 | semidirect |
| 165. C32 | #3417 | semidirect |
| 189. C3 | #84017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5753 | 2 |
| #10592839 | 2 |
| C2×#63550 | 2 |
| #10590636 | 2 |
| #10590629 | 2 |
| #84017 | 3 |