Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
364 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 134 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. #10588384 | C3 | direct (N × H) |
| 15. C3×Dic36 | C4 | semidirect |
| 55. Dic36 | C3×C4 | semidirect |
| 136. C3×C9 | #441 | semidirect |
| 189. C9 | C3×#441 | semidirect |
| 211. C3 | #10588384 | 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×C4×Dic18 | 2 |
| C3×C9×#97 | 2 |
| C3×#63377 | 2 |
| C3×#63376 | 2 |
| C3×#4716 | 3 |
| #10588384 | 3 |