Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
356 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 93 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. #11720935 | C2 | semidirect |
| 5. #11720279 | C2 | semidirect |
| 6. Dic9⋊(C3⋊C8) | C2 | semidirect |
| 7. #11720265 | C2 | semidirect |
| 197. C3×C9 | #478 | semidirect |
| 282. C9 | #5009 | semidirect |
| 319. C3 | #10588446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×Dic9 | 2 |
| #11720935 | 2 |
| #11720576 | 2 |
| C9×#832 | 2 |
| #11720279 | 2 |
| Dic9⋊(C3⋊C8) | 2 |
| #11720265 | 2 |
| #10591411 | 3 |
| #10588446 | 3 |