Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2783 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 2783 conjugacy classes of subgroups — too many to draw. Only its 245 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×C22⋊C4×H(3,𝔽3) | C2 | semidirect |
| 3. C2×#88552 | C2 | semidirect |
| 4. C2×#88542 | C2 | semidirect |
| 10. C23×#272 | C4 | semidirect |
| 12. C22×C4×H(3,𝔽3) | C22 | semidirect |
| 13. C22×#1084 | C22 | semidirect |
| 18. C2×C32×C22⋊C4 | D3 | semidirect |
| 47. C22×C32×C4 | C2×D3 | semidirect |
| 55. C22×H(3,𝔽3) | C22⋊C4 | semidirect |
| 65. C2×#272 | C22⋊C4 | semidirect |
| 126. C22×C32 | (C2×D3)⋊C4 | semidirect |
| 142. C2×C22⋊C4 | #272 | semidirect |
| 143. H(3,𝔽3) | #379 | semidirect |
| 193. C22×C4 | C2×#272 | semidirect |
| 229. C32 | #4955 | semidirect |
| 269. C22 | #88542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#272 | 2 |
| C2×C22⋊C4×H(3,𝔽3) | 2 |
| C2×#88552 | 2 |
| C2×#88542 | 2 |
| C3×#4955 | 3 |