Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
720 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 241 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 |
|---|---|---|
| 4. #10589348 | C2 | semidirect |
| 178. C32 | #1546 | semidirect |
| 213. C3 | #70506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64078 | 2 |
| C32×#423 | 2 |
| #10592624 | 2 |
| #10589348 | 2 |
| #70506 | 3 |