Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
314 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 77 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. #11721773 | C2 | semidirect |
| 2. C9×#904 | C2 | semidirect |
| 3. C2×C3×C9⋊C16 | C2 | semidirect |
| 4. #11720245 | C2 | semidirect |
| 5. #11720243 | C2 | semidirect |
| 6. #11720241 | C2 | semidirect |
| 7. #11720239 | C2 | semidirect |
| 35. C2×C9⋊C16 | D3 | semidirect |
| 87. #904 | D9 | semidirect |
| 185. C3×C9 | #508 | semidirect |
| 258. C9 | #4904 | semidirect |
| 289. C3 | #10588874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721773 | 2 |
| C9×#904 | 2 |
| C2×C3×C9⋊C16 | 2 |
| #11720245 | 2 |
| #11720243 | 2 |
| #11720241 | 2 |
| #11720239 | 2 |
| #10590632 | 3 |
| #10588874 | 3 |