Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
294 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 24. #3746 | C8 | semidirect |
| 107. C32 | #1332 | semidirect |
| 130. 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 |
| C32×C4×C16 | 2 |
| #10589324 | 2 |
| #67505 | 3 |