Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
| 117. C32 | #1340 | semidirect |
| 142. C3 | #67536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592836 | 2 |
| C32×#349 | 2 |
| #10589423 | 2 |
| #67536 | 3 |