Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
263 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 263 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 8. C2×#3746 | C4 | semidirect |
| 10. #63644 | C4 | semidirect |
| 196. C32 | #1340 | semidirect |
| 228. C3 | #67482 | semidirect |
| 229. C3 | #67536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592836 | 2 |
| C3×#4557 | 2 |
| C3×#4553 | 2 |
| #67536 | 3 |
| #67482 | 3 |