Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
780 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 179 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. #10592818 | C2 | semidirect |
| 5. #10592698 | C2 | semidirect |
| 6. C32×#344 | C2 | semidirect |
| 7. #10589425 | C2 | semidirect |
| 28. C3×#344 | D3 | semidirect |
| 103. #344 | C3⋊D3 | semidirect |
| 230. C32 | #1868 | semidirect |
| 272. C3 | #69034 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596216 | 2 |
| #10592828 | 2 |
| #10592818 | 2 |
| #10592705 | 2 |
| #10592698 | 2 |
| C32×#344 | 2 |
| #10589425 | 2 |
| #69034 | 3 |