Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1052 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 1052 conjugacy classes of subgroups — too many to draw. Only its 220 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. C3×C8×C3⋊Dic3 | C2 | semidirect |
| 5. C32×#815 | C2 | semidirect |
| 6. #11722020 | C2 | semidirect |
| 7. Dic3×C3⋊(C3⋊C8) | C2 | semidirect |
| 13. #88850 | C4 | semidirect |
| 20. #88785 | C4 | semidirect |
| 30. C8×C3⋊Dic3 | D3 | semidirect |
| 32. C3×#815 | D3 | semidirect |
| 93. #815 | C3⋊D3 | semidirect |
| 186. C33 | #405 | semidirect |
| 259. C32 | #4689 | semidirect |
| 260. C32 | #4708 | semidirect |
| 290. C3 | #10590910 | semidirect |
| 291. C3 | #10592407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88850 | 2 |
| #11723452 | 2 |
| C2×#88785 | 2 |
| C3×C8×C3⋊Dic3 | 2 |
| C32×#815 | 2 |
| #11722020 | 2 |
| Dic3×C3⋊(C3⋊C8) | 2 |
| #10592407 | 3 |
| #10590910 | 3 |