Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1259 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 1259 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×C8×#272 | C2 | semidirect |
| 3. C2×#3745⋊C3 | C2 | semidirect |
| 4. C2×#88432 | C2 | semidirect |
| 5. #11720838 | C2 | direct (N × H) |
| 9. C2×C4⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 12. #88655 | C22 | semidirect |
| 13. C2×C8×H(3,𝔽3) | C22 | semidirect |
| 14. C2×#6180 | C22 | semidirect |
| 15. C8×#272 | C22 | semidirect |
| 16. #3745⋊C3 | C22 | semidirect |
| 17. #88432 | C22 | semidirect |
| 19. C2×#3745 | D3 | semidirect |
| 34. C4⋊((C3⋊D3)⋊C3) | C23 | semidirect |
| 36. C8×H(3,𝔽3) | C23 | semidirect |
| 37. #6180 | C23 | semidirect |
| 41. C2×C4⋊(C3⋊D3) | C2×D3 | semidirect |
| 49. C2×C32×C8 | C2×D3 | semidirect |
| 50. #3745 | C2×D3 | semidirect |
| 58. C2×#272 | D8 | semidirect |
| 87. C4⋊(C3⋊D3) | C22×D3 | semidirect |
| 98. C32×C8 | C22×D3 | semidirect |
| 102. C2×H(3,𝔽3) | C2×D8 | semidirect |
| 104. #272 | C2×D8 | semidirect |
| 156. H(3,𝔽3) | C22×D8 | semidirect |
| 195. C2×C32 | D3×D8 | semidirect |
| 211. C2×C8 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 239. C32 | C2×D3×D8 | semidirect |
| 252. C8 | C2×((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 279. C2 | #11720838 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88655 | 2 |
| C2×C8×#272 | 2 |
| C2×#3745⋊C3 | 2 |
| C2×#88432 | 2 |
| #11720838 | 2 |
| C2×D3×D24 | 3 |