Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
828 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 15. C2×#3746 | C4 | semidirect |
| 191. C32 | #1979 | semidirect |
| 225. C3 | #70710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3746 | 2 |
| C2×C32×#108 | 2 |
| C2×#63651 | 2 |
| #10592819 | 2 |
| #10592800 | 2 |
| #70710 | 3 |