Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2519 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 2519 conjugacy classes of subgroups — too many to draw. Only its 292 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. C2×#3757⋊C3 | C2 | semidirect |
| 3. #10592946 | C3 | semidirect |
| 6. C24×H(3,𝔽3) | C4 | semidirect |
| 8. C22×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 13. C2×#3757 | C2×C3 | semidirect |
| 30. C24×C32 | Dic3 | semidirect |
| 31. C24×C32 | C3×C4 | semidirect |
| 34. C22×C3⋊Dic3 | C22×C3 | semidirect |
| 41. C22×H(3,𝔽3) | C22⋊C4 | semidirect |
| 106. C22×C32 | #217 | semidirect |
| 107. C22×C32 | C3×C22⋊C4 | semidirect |
| 116. H(3,𝔽3) | #379 | semidirect |
| 154. C24 | (C3⋊Dic3)⋊C3 | semidirect |
| 186. C32 | #5247 | semidirect |
| 187. C32 | C3×#379 | semidirect |
| 210. C22 | #3757⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×H(3,𝔽3) | 2 |
| C2×#3757⋊C3 | 2 |
| #10592946 | 3 |
| C3×#5247 | 3 |