Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
315 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 315 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 215. C32 | #1307 | semidirect |
| 254. C3 | #67716 | semidirect |
| 255. C3 | #67758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592625 | 2 |
| C3×#4926 | 2 |
| C3×#4924 | 2 |
| #67758 | 3 |
| #67716 | 3 |