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 |
|---|---|---|
| 3. #10592730 | C2 | semidirect |
| 4. Q8×C3⋊(C3⋊C8) | C2 | semidirect |
| 6. #10589348 | C2 | semidirect |
| 7. #10589345 | C2 | semidirect |
| 193. C32 | #1682 | semidirect |
| 231. C3 | #71023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#460 | 2 |
| #10592769 | 2 |
| #10592730 | 2 |
| Q8×C3⋊(C3⋊C8) | 2 |
| #10589410 | 2 |
| #10589348 | 2 |
| #10589345 | 2 |
| #71023 | 3 |