Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
813 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 813 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 1. C22×#3746 | C2 | semidirect |
| 4. C2×#63561 | C2 | semidirect |
| 5. C3×#4552 | C2 | semidirect |
| 31. #4552 | D3 | semidirect |
| 308. C32 | #2020 | semidirect |
| 353. C3 | #68944 | semidirect |
| 354. C3 | #70008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3746 | 2 |
| C2×#63831 | 2 |
| C3×#5110 | 2 |
| C2×#63561 | 2 |
| C3×#4552 | 2 |
| #70008 | 3 |
| #68944 | 3 |