Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1851 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1851 conjugacy classes of subgroups — too many to draw. Only its 187 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. C2×#88655 | C2 | semidirect |
| 2. C42×#272 | C2 | semidirect |
| 3. #11721385 | C2 | semidirect |
| 4. #11721144 | C2 | semidirect |
| 8. C2×C4⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 9. C2×#6198 | C22 | semidirect |
| 11. C42×H(3,𝔽3) | C22 | semidirect |
| 12. C4×#1084 | C22 | semidirect |
| 14. #64083 | D3 | semidirect |
| 24. C4×#272 | D4 | semidirect |
| 30. C2×C4⋊(C3⋊D3) | C2×D3 | semidirect |
| 37. C32×C42 | C2×D3 | semidirect |
| 44. C4×H(3,𝔽3) | C2×D4 | semidirect |
| 45. #1084 | C2×D4 | semidirect |
| 72. #272 | #127 | semidirect |
| 100. C32×C4 | D3×D4 | semidirect |
| 107. H(3,𝔽3) | C2×#127 | semidirect |
| 142. C42 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 161. C32 | D3×#127 | semidirect |
| 184. C4 | #88655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88655 | 2 |
| C42×#272 | 2 |
| #11721385 | 2 |
| #11721144 | 2 |
| D3×#874 | 3 |