Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
312 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 9. #10588477 | C3 | direct (N × H) |
| 191. C3×C9 | #491 | semidirect |
| 269. C9 | C3×#491 | semidirect |
| 302. C3 | #10588477 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63506 | 2 |
| C3×#63452 | 2 |
| C3×C9×#103 | 2 |
| C3×#63395 | 2 |
| C3×#63376 | 2 |
| C3×#63375 | 2 |
| C3×#63368 | 2 |
| C3×#4797 | 3 |
| #10588477 | 3 |