Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
540 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 2. #11721744 | C2 | semidirect |
| 5. #11720541 | C2 | semidirect |
| 6. #11720537 | C2 | semidirect |
| 7. #11720525 | C2 | semidirect |
| 37. C3×D4×C9 | Q8 | semidirect |
| 112. D4×C9 | Dic6 | semidirect |
| 179. C3×C9 | #474 | semidirect |
| 184. C3×D4 | Dic18 | semidirect |
| 248. C9 | #4759 | semidirect |
| 252. D4 | #6226 | semidirect |
| 281. C3 | #10588439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C3⋊Dic9 | 2 |
| #11721744 | 2 |
| C3×C9×#102 | 2 |
| #11720576 | 2 |
| #11720541 | 2 |
| #11720537 | 2 |
| #11720525 | 2 |
| #10592458 | 3 |
| #10588439 | 3 |