Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
492 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 107 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. C4×C9×Dic6 | C2 | semidirect |
| 3. C2×#88426 | C2 | semidirect |
| 4. C3×C4⋊(C9⋊C8) | C2 | semidirect |
| 5. #11720267 | C2 | semidirect |
| 28. C4⋊(C9⋊C8) | D3 | semidirect |
| 40. C9×Dic6 | D4 | semidirect |
| 73. C3×C4×C9 | SD16 | semidirect |
| 84. C4×Dic6 | D9 | semidirect |
| 177. C4×C9 | #204 | semidirect |
| 185. C3×C9 | #460 | semidirect |
| 217. Dic6 | D36 | semidirect |
| 262. C3×C4 | #3675 | semidirect |
| 272. C9 | #4848 | semidirect |
| 305. C4 | #88426 | semidirect |
| 309. C3 | #10588710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721711 | 2 |
| C4×C9×Dic6 | 2 |
| C2×#88426 | 2 |
| C3×C4⋊(C9⋊C8) | 2 |
| #11720267 | 2 |
| #10590367 | 3 |
| #10588710 | 3 |