Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1602 conjugacy classes of subgroups; only the 314 normal subgroups are shown.
This group has 1602 conjugacy classes of subgroups — too many to draw. Only its 314 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×C3×D4×D9 | C2 | semidirect |
| 2. C3×C9×#127 | C2 | semidirect |
| 3. C3×#63502 | C2 | semidirect |
| 4. C3×#63436 | C2 | semidirect |
| 5. C3×C42×D9 | C2 | semidirect |
| 7. D9×#127 | C3 | direct (N × H) |
| 9. C2×C3×D4×C9 | C22 | semidirect |
| 10. C2×C3×#611 | C22 | semidirect |
| 12. C2×C3×D36 | C22 | semidirect |
| 14. C3×C42×C9 | C22 | semidirect |
| 15. C3×C4×Dic9 | C22 | semidirect |
| 21. C2×D4×D9 | C2×C3 | semidirect |
| 23. C9×#127 | C2×C3 | semidirect |
| 24. #63502 | C2×C3 | semidirect |
| 25. #63436 | C2×C3 | semidirect |
| 26. C42×D9 | C2×C3 | semidirect |
| 36. C3×C4×D9 | D4 | semidirect |
| 49. C2×D4×C9 | C22×C3 | semidirect |
| 50. C2×#611 | C22×C3 | semidirect |
| 52. C2×D36 | C22×C3 | semidirect |
| 55. C42×C9 | C22×C3 | semidirect |
| 56. C4×Dic9 | C22×C3 | semidirect |
| 62. C3×C4×C9 | C2×D4 | semidirect |
| 63. C3×Dic9 | C2×D4 | semidirect |
| 69. C3×#127 | D9 | direct (N × H) |
| 97. C4×D9 | C3×D4 | semidirect |
| 102. C3×D9 | #127 | direct (N × H) |
| 109. C2×C3×D4 | C2×D9 | semidirect |
| 118. C3×C42 | C2×D9 | semidirect |
| 136. C4×C9 | C2×C3×D4 | semidirect |
| 137. Dic9 | C2×C3×D4 | semidirect |
| 141. #127 | C3×D9 | direct (N × H) |
| 143. C3×C9 | C2×#127 | semidirect |
| 176. D9 | C3×#127 | direct (N × H) |
| 181. C2×D4 | C2×C3×D9 | semidirect |
| 184. C42 | C2×C3×D9 | semidirect |
| 199. C3×C4 | D4×D9 | semidirect |
| 204. C9 | C2×C3×#127 | semidirect |
| 231. C4 | C3×D4×D9 | semidirect |
| 233. C3 | D9×#127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×D9 | 2 |
| C3×C9×#127 | 2 |
| C3×#63502 | 2 |
| C3×#63436 | 2 |
| C3×C42×D9 | 2 |
| C3×D3×#127 | 3 |
| D9×#127 | 3 |