Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
420 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 174. C32 | #1704 | semidirect |
| 205. C3 | #68555 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592550 | 2 |
| #10592549 | 2 |
| #10592380 | 2 |
| #10592378 | 2 |
| C32×#334 | 2 |
| #10589352 | 2 |
| #10589347 | 2 |
| #68555 | 3 |