Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
716 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 222 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 |
| 2. C3×#63458 | C2 | semidirect |
| 3. C3×#63457 | C2 | semidirect |
| 4. C3×#63456 | C2 | semidirect |
| 5. C3×#63437 | C2 | semidirect |
| 7. #10589802 | C3 | direct (N × H) |
| 25. C9×#125 | C2×C3 | semidirect |
| 26. #63458 | C2×C3 | semidirect |
| 27. #63457 | C2×C3 | semidirect |
| 28. #63456 | C2×C3 | semidirect |
| 29. #63437 | C2×C3 | semidirect |
| 75. C3×#125 | D9 | semidirect |
| 155. #125 | C3×D9 | semidirect |
| 160. C3×C9 | #562 | semidirect |
| 223. C9 | C3×#562 | semidirect |
| 250. C3 | #10589802 | 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×#63458 | 2 |
| C3×#63457 | 2 |
| C3×#63456 | 2 |
| C3×#63437 | 2 |
| C3×#5700 | 3 |
| #10589802 | 3 |