Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
341 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 88 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. #10592895 | C2 | semidirect |
| 3. #10590919 | C2 | semidirect |
| 4. C3×#4567 | C2 | semidirect |
| 5. #10589143 | C2 | semidirect |
| 6. #10589121 | C2 | semidirect |
| 7. #10589104 | C2 | semidirect |
| 17. C3×#829 | C4 | semidirect |
| 18. C3×#828 | C4 | semidirect |
| 19. C3×#827 | C4 | semidirect |
| 20. C3×#826 | C4 | semidirect |
| 34. #4567 | D3 | semidirect |
| 82. #829 | Dic3 | semidirect |
| 83. #828 | Dic3 | semidirect |
| 84. #827 | Dic3 | semidirect |
| 85. #826 | Dic3 | semidirect |
| 281. C32 | #2179 | semidirect |
| 318. C3 | #69239 | semidirect |
| 319. C3 | #71512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592895 | 2 |
| C3×#5194 | 2 |
| #10590919 | 2 |
| C3×#4567 | 2 |
| #10589143 | 2 |
| #10589121 | 2 |
| #10589104 | 2 |
| #71512 | 3 |
| #69239 | 3 |