Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
942 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 942 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 |
|---|---|---|
| 2. #10595987 | C2 | semidirect |
| 5. C2×#63651 | C2 | semidirect |
| 6. #10589423 | C2 | semidirect |
| 7. #10589397 | C2 | semidirect |
| 13. #64153 | C4 | semidirect |
| 14. #64145 | C4 | semidirect |
| 273. C32 | #1912 | semidirect |
| 323. C3 | #70411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596296 | 2 |
| #10595987 | 2 |
| C32×#421 | 2 |
| #10592935 | 2 |
| C2×#63651 | 2 |
| #10589423 | 2 |
| #10589397 | 2 |
| #70411 | 3 |