Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
690 conjugacy classes of subgroups; only the 311 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 311 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 |
| 23. C42×C9 | Dic3 | semidirect |
| 47. C3×C42 | Dic9 | semidirect |
| 59. C3×C9 | #383 | semidirect |
| 74. C42 | C3⋊Dic9 | semidirect |
| 84. C9 | #4937 | semidirect |
| 97. C3 | #10588617 | 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 |
| #11720572 | 2 |
| #10592636 | 3 |
| #10588617 | 3 |