Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
366 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 7. #10588553 | C3 | direct (N × H) |
| 15. C3×Dic36 | C4 | semidirect |
| 55. Dic36 | C3×C4 | semidirect |
| 62. C3×Dic9 | Q16 | semidirect |
| 134. Dic9 | C3×Q16 | semidirect |
| 140. C3×C9 | C4×Q16 | semidirect |
| 199. C9 | C3×C4×Q16 | semidirect |
| 226. C3 | #10588553 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic36 | 2 |
| C3×#63449 | 2 |
| C3×C9×#107 | 2 |
| C3×C8×Dic9 | 2 |
| C3×#63368 | 2 |
| C3×#4873 | 3 |
| #10588553 | 3 |