Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1087 conjugacy classes of subgroups; only the 452 normal subgroups are shown.
This group has 1087 conjugacy classes of subgroups — too many to draw. Only its 452 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. Q8×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 4. #10596283 | C3 | semidirect |
| 6. C2×Q8×H(3,𝔽3) | C4 | semidirect |
| 15. Q8×C3⋊Dic3 | C2×C3 | semidirect |
| 29. C2×C32×Q8 | Dic3 | semidirect |
| 30. C2×C32×Q8 | C3×C4 | semidirect |
| 113. H(3,𝔽3) | #519 | semidirect |
| 142. C2×Q8 | (C3⋊Dic3)⋊C3 | semidirect |
| 168. C32 | #5812 | semidirect |
| 169. C32 | C3×#519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×H(3,𝔽3) | 2 |
| Q8×(C3⋊Dic3)⋊C3 | 2 |
| #64135⋊C3 | 2 |
| #10596283 | 3 |
| C3×#5812 | 3 |