Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
492 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 4. #11720539 | C2 | semidirect |
| 5. C3×#63376 | C2 | semidirect |
| 6. #11720277 | C2 | semidirect |
| 7. #11720276 | C2 | semidirect |
| 16. D3×Dic18 | C4 | semidirect |
| 38. #63376 | D3 | semidirect |
| 225. C3×C9 | #419 | semidirect |
| 320. C9 | #4802 | semidirect |
| 361. C3 | #10588804 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Dic18 | 2 |
| C2×C9×ΓL(1,𝔽25) | 2 |
| #11720906 | 2 |
| #11720539 | 2 |
| C3×#63376 | 2 |
| #11720277 | 2 |
| #11720276 | 2 |
| #10590948 | 3 |
| #10588804 | 3 |