Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
528 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 129 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×#486 | C2 | semidirect |
| 2. #10592783 | C2 | semidirect |
| 4. C8×C4⋊(C3⋊D3) | C2 | semidirect |
| 5. #10589412 | C2 | semidirect |
| 6. #10589410 | C2 | semidirect |
| 7. #10589323 | C2 | semidirect |
| 24. C3×#486 | D3 | semidirect |
| 87. #486 | C3⋊D3 | semidirect |
| 200. C32 | #1677 | semidirect |
| 242. C3 | #71200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#486 | 2 |
| #10592783 | 2 |
| #10592771 | 2 |
| C8×C4⋊(C3⋊D3) | 2 |
| #10589412 | 2 |
| #10589410 | 2 |
| #10589323 | 2 |
| #71200 | 3 |