Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 139 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. C32×#462 | C2 | semidirect |
| 4. Q8×C3⋊(C3⋊C8) | C2 | semidirect |
| 5. #10589413 | C2 | semidirect |
| 7. #10589345 | C2 | semidirect |
| 24. C3×#462 | D3 | semidirect |
| 87. #462 | C3⋊D3 | semidirect |
| 193. C32 | #1682 | semidirect |
| 231. C3 | #71055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#462 | 2 |
| #10592787 | 2 |
| #10592726 | 2 |
| Q8×C3⋊(C3⋊C8) | 2 |
| #10589413 | 2 |
| #10589351 | 2 |
| #10589345 | 2 |
| #71055 | 3 |