Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
310 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 58 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×C9×#99 | C2 | semidirect |
| 3. C3×#63393 | C2 | semidirect |
| 5. #10588151 | C3 | direct (N × H) |
| 9. C2×C3×D36 | C4 | semidirect |
| 12. C3×C4×Dic9 | C4 | semidirect |
| 18. C9×#99 | C2×C3 | semidirect |
| 19. #63393 | C2×C3 | semidirect |
| 44. C2×D36 | C3×C4 | semidirect |
| 48. C4×Dic9 | C3×C4 | semidirect |
| 65. C3×#99 | D9 | semidirect |
| 150. #99 | C3×D9 | semidirect |
| 151. C3×C9 | #353 | semidirect |
| 233. C9 | C3×#353 | semidirect |
| 272. C3 | #10588151 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63502 | 2 |
| C3×C9×#99 | 2 |
| C3×#63393 | 2 |
| C3×#4474 | 3 |
| #10588151 | 3 |