Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
432 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 149 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 | #70947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C8×Q8 | 2 |
| #10592720 | 2 |
| #10592719 | 2 |
| #10592380 | 2 |
| #10589348 | 2 |
| #10589347 | 2 |
| #10589324 | 2 |
| #70947 | 3 |