Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
314 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 57 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. #11721805 | C2 | semidirect |
| 2. #11720824 | C2 | semidirect |
| 3. C9×#828 | C2 | semidirect |
| 4. C3×#63388 | C2 | semidirect |
| 5. #11720239 | C2 | semidirect |
| 6. #11720234 | C2 | semidirect |
| 7. (C3⋊D9)⋊C16 | C2 | semidirect |
| 32. #63388 | D3 | semidirect |
| 92. #828 | D9 | semidirect |
| 185. C3×C9 | #508 | semidirect |
| 258. C9 | #4919 | semidirect |
| 289. C3 | #10588596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721805 | 2 |
| #11720824 | 2 |
| C9×#828 | 2 |
| C3×#63388 | 2 |
| #11720239 | 2 |
| #11720234 | 2 |
| (C3⋊D9)⋊C16 | 2 |
| #10591049 | 3 |
| #10588596 | 3 |