Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
550 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 102 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×#63710 | C2 | semidirect |
| 2. C3×#63502 | C2 | semidirect |
| 3. C3×#63470 | C2 | semidirect |
| 4. C3×C9×#100 | C2 | semidirect |
| 5. C3×#63384 | C2 | semidirect |
| 7. #10588427 | C3 | direct (N × H) |
| 14. C2×C3×D36 | C22 | semidirect |
| 15. C3×C9×M16 | C22 | semidirect |
| 16. C3×C4×Dic9 | C22 | semidirect |
| 22. #63710 | C2×C3 | semidirect |
| 25. #63502 | C2×C3 | semidirect |
| 26. #63470 | C2×C3 | semidirect |
| 28. C9×#100 | C2×C3 | semidirect |
| 29. #63384 | C2×C3 | semidirect |
| 41. C3×D36 | D4 | semidirect |
| 43. C3×Dic18 | D4 | semidirect |
| 65. C2×D36 | C22×C3 | semidirect |
| 67. C9×M16 | C22×C3 | semidirect |
| 68. C4×Dic9 | C22×C3 | semidirect |
| 89. C3×#100 | D9 | semidirect |
| 121. D36 | C3×D4 | semidirect |
| 123. Dic18 | C3×D4 | semidirect |
| 150. C3×M16 | C2×D9 | semidirect |
| 184. #100 | C3×D9 | semidirect |
| 185. C3×C9 | #453 | semidirect |
| 242. M16 | C2×C3×D9 | semidirect |
| 270. C9 | C3×#453 | semidirect |
| 310. C3 | #10588427 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63710 | 2 |
| C3×#63502 | 2 |
| C3×#63470 | 2 |
| C3×C9×#100 | 2 |
| C3×#63384 | 2 |
| C3×#4747 | 3 |
| #10588427 | 3 |