Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
348 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 114 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×#63469 | C2 | semidirect |
| 3. C3×C9×#108 | C2 | semidirect |
| 4. C3×#63384 | C2 | semidirect |
| 5. C3×C8×Dic9 | C2 | semidirect |
| 7. #10588575 | C3 | direct (N × H) |
| 13. C3×D72 | C4 | semidirect |
| 14. C3×#3664 | C4 | semidirect |
| 17. C3×Dic36 | C4 | semidirect |
| 23. #63469 | C2×C3 | semidirect |
| 26. C9×#108 | C2×C3 | semidirect |
| 27. #63384 | C2×C3 | semidirect |
| 28. C8×Dic9 | C2×C3 | semidirect |
| 59. D72 | C3×C4 | semidirect |
| 60. #3664 | C3×C4 | semidirect |
| 63. Dic36 | C3×C4 | semidirect |
| 75. C3×#108 | D9 | semidirect |
| 150. #108 | C3×D9 | semidirect |
| 153. C3×C9 | #443 | semidirect |
| 215. C9 | C3×#443 | semidirect |
| 242. C3 | #10588575 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63469 | 2 |
| C3×#63467 | 2 |
| C3×C9×#108 | 2 |
| C3×#63384 | 2 |
| C3×C8×Dic9 | 2 |
| C3×#4895 | 3 |
| #10588575 | 3 |