Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
490 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 231 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 |
|---|---|---|
| 22. C3×C8×C9 | Q8 | semidirect |
| 57. C8×C9 | Dic6 | semidirect |
| 85. C3×C9 | #500 | semidirect |
| 96. C3×C8 | Dic18 | semidirect |
| 120. C9 | #4682 | semidirect |
| 126. C8 | #6226 | semidirect |
| 138. C3 | #10588362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721706 | 2 |
| C3×C4×C8×C9 | 2 |
| #11720541 | 2 |
| #10592381 | 3 |
| #10588362 | 3 |