Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
763 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 763 conjugacy classes of subgroups — too many to draw. Only its 126 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×C3×Dic12 | C2 | semidirect |
| 4. C2×#63560 | C2 | semidirect |
| 5. C3×#4552 | C2 | semidirect |
| 24. C22×Dic12 | D3 | semidirect |
| 31. #4552 | D3 | semidirect |
| 311. C32 | #2020 | semidirect |
| 357. C3 | #68944 | semidirect |
| 358. C3 | #72074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic12 | 2 |
| C2×#63833 | 2 |
| #10592809 | 2 |
| C2×#63560 | 2 |
| C3×#4552 | 2 |
| #72074 | 3 |
| #68944 | 3 |