Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1050 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 285 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×#578 | C2 | semidirect |
| 2. #10596224 | C2 | semidirect |
| 3. #10592894 | C2 | semidirect |
| 4. #10592893 | C2 | semidirect |
| 5. C2×#63656 | C2 | semidirect |
| 6. #10592878 | C2 | semidirect |
| 7. #10592839 | C2 | semidirect |
| 25. C3×#578 | D3 | semidirect |
| 88. #578 | C3⋊D3 | semidirect |
| 187. C32 | #3417 | semidirect |
| 216. C3 | #84017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#578 | 2 |
| #10596224 | 2 |
| #10592894 | 2 |
| #10592893 | 2 |
| C2×#63656 | 2 |
| #10592878 | 2 |
| #10592839 | 2 |
| #84017 | 3 |