Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
218 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 218 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 |
|---|---|---|
| 5. #10588154 | C3 | direct (N × H) |
| 121. C3×C9 | #356 | semidirect |
| 176. C9 | C3×#356 | semidirect |
| 199. C3 | #10588154 | 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×C9×#101 | 2 |
| C3×#63394 | 2 |
| C3×#4478 | 3 |
| #10588154 | 3 |