Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
251 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 251 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 28. #3746 | C8 | semidirect |
| 181. C32 | #1332 | semidirect |
| 211. C3 | #67472 | semidirect |
| 212. C3 | #67505 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3746 | 2 |
| C3×C4×C3⋊C16 | 2 |
| C3×#4458 | 2 |
| #67505 | 3 |
| #67472 | 3 |