Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
342 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 87 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. #11720927 | C2 | semidirect |
| 3. #11720541 | C2 | semidirect |
| 5. C9×Dic3⋊C8 | C2 | semidirect |
| 7. #11720278 | C2 | semidirect |
| 99. Dic3⋊C8 | D9 | semidirect |
| 193. C3×C9 | #478 | semidirect |
| 273. C9 | #4766 | semidirect |
| 309. C3 | #10588531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic3×D36 | 2 |
| #11720927 | 2 |
| #11720541 | 2 |
| C3×#63380 | 2 |
| C9×Dic3⋊C8 | 2 |
| #11720283 | 2 |
| #11720278 | 2 |
| #10590767 | 3 |
| #10588531 | 3 |