Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
236 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 2. C3×#63377 | C2 | semidirect |
| 3. C3×#63371 | C2 | semidirect |
| 5. #10588243 | C3 | direct (N × H) |
| 7. C3×C9×Q16 | C4 | semidirect |
| 9. C3×C9×D8 | C4 | semidirect |
| 18. #63377 | C2×C3 | semidirect |
| 19. #63371 | C2×C3 | semidirect |
| 40. C9×Q16 | C3×C4 | semidirect |
| 44. C9×D8 | C3×C4 | semidirect |
| 93. C3×Q16 | Dic9 | semidirect |
| 99. C3×D8 | Dic9 | semidirect |
| 128. C3×C9 | #360 | semidirect |
| 162. Q16 | C3×Dic9 | semidirect |
| 164. D8 | C3×Dic9 | semidirect |
| 187. C9 | C3×#360 | semidirect |
| 212. C3 | #10588243 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#135 | 2 |
| C3×#63377 | 2 |
| C3×#63371 | 2 |
| C3×#4566 | 3 |
| #10588243 | 3 |