Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
588 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 203. C32 | #2070 | semidirect |
| 237. C3 | #70732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#430 | 2 |
| C2×#63651 | 2 |
| #10592824 | 2 |
| #10592823 | 2 |
| #10589426 | 2 |
| #70732 | 3 |