Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
386 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 1. C3×C9×#125 | C2 | semidirect |
| 3. C3×#63369 | C2 | semidirect |
| 4. C3×#63362 | C2 | semidirect |
| 6. #10588748 | C3 | direct (N × H) |
| 18. C9×#125 | C2×C3 | semidirect |
| 20. #63369 | C2×C3 | semidirect |
| 21. #63362 | C2×C3 | semidirect |
| 54. C3×#125 | D9 | semidirect |
| 114. #125 | C3×D9 | semidirect |
| 117. C3×C9 | #490 | semidirect |
| 167. C9 | C3×#490 | semidirect |
| 190. C3 | #10588748 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#125 | 2 |
| C3×#63436 | 2 |
| C3×#63369 | 2 |
| C3×#63362 | 2 |
| C3×#5067 | 3 |
| #10588748 | 3 |