Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1089 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 1089 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 1. C22×C4⋊#272 | C2 | semidirect |
| 2. #11721830 | C2 | semidirect |
| 3. C2×#88529 | C2 | semidirect |
| 4. H(3,𝔽3)×C22⋊C8 | C2 | semidirect |
| 5. #11720554 | C2 | semidirect |
| 13. C2×C4⋊#272 | C22 | semidirect |
| 14. C2×C8×H(3,𝔽3) | C22 | semidirect |
| 16. C4⋊#1084 | C22 | semidirect |
| 21. C32×C22⋊C8 | D3 | semidirect |
| 37. C4⋊#272 | D4 | semidirect |
| 48. C2×C32×C8 | C2×D3 | semidirect |
| 54. C22×H(3,𝔽3) | D8 | semidirect |
| 123. C22×C32 | D24 | semidirect |
| 139. C22⋊C8 | #272 | semidirect |
| 140. H(3,𝔽3) | #447 | semidirect |
| 187. C2×C8 | C2×#272 | semidirect |
| 218. C32 | #4732 | semidirect |
| 256. C22 | #88529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#272 | 2 |
| #11721830 | 2 |
| C2×#88529 | 2 |
| H(3,𝔽3)×C22⋊C8 | 2 |
| #11720554 | 2 |
| C3×#4732 | 3 |