Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
660 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 150 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. C2×D8×D9 | C2 | semidirect |
| 2. C2×C9×D16 | C2 | semidirect |
| 3. C2×#63385 | C2 | semidirect |
| 4. D9×D16 | C2 | direct (N × H) |
| 5. C2×D144 | C2 | semidirect |
| 6. C2×C16×D9 | C2 | semidirect |
| 9. C2×C9×D8 | C22 | semidirect |
| 12. D8×D9 | C22 | semidirect |
| 13. C2×D72 | C22 | semidirect |
| 15. C9×D16 | C22 | semidirect |
| 16. C2×C9×C16 | C22 | semidirect |
| 17. #63385 | C22 | semidirect |
| 18. C2×C9⋊C16 | C22 | semidirect |
| 19. D144 | C22 | semidirect |
| 20. C16×D9 | C22 | semidirect |
| 35. C9×D8 | C23 | semidirect |
| 40. D72 | C23 | semidirect |
| 43. C9×C16 | C23 | semidirect |
| 44. C9⋊C16 | C23 | semidirect |
| 80. C2×D16 | D9 | direct (N × H) |
| 106. C2×D9 | D16 | direct (N × H) |
| 116. C2×D8 | C2×D9 | semidirect |
| 120. D16 | C2×D9 | direct (N × H) |
| 123. C2×C16 | C2×D9 | semidirect |
| 142. C2×C9 | C2×D16 | semidirect |
| 145. D9 | C2×D16 | direct (N × H) |
| 157. D8 | C22×D9 | semidirect |
| 163. C16 | C22×D9 | semidirect |
| 175. C9 | C22×D16 | semidirect |
| 213. C2 | D9×D16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D9 | 2 |
| C2×C9×D16 | 2 |
| C2×#63385 | 2 |
| D9×D16 | 2 |
| C2×D144 | 2 |
| C2×C16×D9 | 2 |
| C2×D3×D16 | 3 |