Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
310 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 53 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. #11720577 | C2 | semidirect |
| 3. C9×#834 | C2 | semidirect |
| 9. C2×C3×D36 | C4 | semidirect |
| 12. C3×C4×Dic9 | C4 | semidirect |
| 44. C2×D36 | Dic3 | semidirect |
| 48. C4×Dic9 | Dic3 | semidirect |
| 67. #834 | D9 | semidirect |
| 151. C3×C9 | #353 | semidirect |
| 233. C9 | #4545 | semidirect |
| 272. C3 | #10588151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63502 | 2 |
| #11720577 | 2 |
| C9×#834 | 2 |
| #10589178 | 3 |
| #10588151 | 3 |