Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
720 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 13. #64078 | C4 | semidirect |
| 14. #64078 | C4 | semidirect |
| 16. C4×#634 | C4 | semidirect |
| 194. C32 | #1503 | semidirect |
| 233. C3 | #69471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595941 | 2 |
| C32×C4×C4⋊C4 | 2 |
| #10592624 | 2 |
| #10589318 | 2 |
| #69471 | 3 |