Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
360 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 1. C9×#888 | C2 | semidirect |
| 3. #11720525 | C2 | semidirect |
| 6. #11720262 | C2 | semidirect |
| 7. Dic3⋊(C9⋊C8) | C2 | semidirect |
| 44. C3×D36 | Q8 | semidirect |
| 89. #888 | D9 | semidirect |
| 127. D36 | Dic6 | semidirect |
| 196. C3×C9 | #474 | semidirect |
| 278. C9 | #4759 | semidirect |
| 315. C3 | #10588772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#888 | 2 |
| Dic3×D36 | 2 |
| #11720525 | 2 |
| C3×#63369 | 2 |
| #11720266 | 2 |
| #11720262 | 2 |
| Dic3⋊(C9⋊C8) | 2 |
| #10590463 | 3 |
| #10588772 | 3 |