Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 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×#500 | C2 | semidirect |
| 4. #10589412 | C2 | semidirect |
| 5. #10589323 | C2 | semidirect |
| 18. C3×#500 | D3 | semidirect |
| 62. #500 | C3⋊D3 | semidirect |
| 142. C32 | #1695 | semidirect |
| 171. C3 | #71374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#500 | 2 |
| #10592783 | 2 |
| #10592387 | 2 |
| #10589412 | 2 |
| #10589323 | 2 |
| #71374 | 3 |