Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
522 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 213 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. C3×C42×C9 | C4 | semidirect |
| 18. #4937 | C9 | direct (N × H) |
| 26. C42×C9 | Dic3 | semidirect |
| 56. C3×C42 | C4×C9 | semidirect |
| 71. C3×C9 | #383 | semidirect |
| 91. C42 | C9×Dic3 | semidirect |
| 105. C9 | #4937 | direct (N × H) |
| 121. C3 | C9×#383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C42×C9 | 2 |
| C9×C3⋊#95 | 2 |
| C3×#4937 | 3 |
| C9×#383 | 3 |