Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
316 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 92 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. C3×#5196 | C2 | semidirect |
| 3. #10590915 | C2 | semidirect |
| 4. #10589433 | C2 | semidirect |
| 5. #10589143 | C2 | semidirect |
| 6. #10589120 | C2 | semidirect |
| 7. #10589103 | C2 | semidirect |
| 17. C3×#829 | C4 | semidirect |
| 18. C3×#828 | C4 | semidirect |
| 19. C3×#827 | C4 | semidirect |
| 20. C3×#826 | C4 | semidirect |
| 28. #5196 | D3 | semidirect |
| 80. #829 | Dic3 | semidirect |
| 81. #828 | Dic3 | semidirect |
| 82. #827 | Dic3 | semidirect |
| 83. #826 | Dic3 | semidirect |
| 272. C32 | #2179 | semidirect |
| 309. C3 | #70922 | semidirect |
| 310. C3 | #71512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5196 | 2 |
| C3×#5194 | 2 |
| #10590915 | 2 |
| #10589433 | 2 |
| #10589143 | 2 |
| #10589120 | 2 |
| #10589103 | 2 |
| #71512 | 3 |
| #70922 | 3 |