Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
432 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 139 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 | #1684 | semidirect |
| 205. C3 | #71151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#477 | 2 |
| #10592792 | 2 |
| Q8×C3⋊(C3⋊C8) | 2 |
| #10592719 | 2 |
| #10589412 | 2 |
| #10589352 | 2 |
| #10589345 | 2 |
| #71151 | 3 |