Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
552 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 19. #63649 | C4 | semidirect |
| 187. C32 | #1953 | semidirect |
| 216. C3 | #69015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592824 | 2 |
| #10592823 | 2 |
| C2×#63649 | 2 |
| #10592696 | 2 |
| C32×#344 | 2 |
| #10589399 | 2 |
| #69015 | 3 |