Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1086 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1086 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×#64153 | C2 | semidirect |
| 4. C32×#419 | C2 | semidirect |
| 6. C2×#63651 | C2 | semidirect |
| 7. #10589398 | C2 | semidirect |
| 33. C3×#419 | D3 | semidirect |
| 139. #419 | C3⋊D3 | semidirect |
| 314. C32 | #2005 | semidirect |
| 371. C3 | #70346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64153 | 2 |
| C2×#64151 | 2 |
| #10595997 | 2 |
| C32×#419 | 2 |
| C2×#63652 | 2 |
| C2×#63651 | 2 |
| #10589398 | 2 |
| #70346 | 3 |