Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
676 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 211 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. C27×#117 | C2 | semidirect |
| 3. #11720175 | C2 | semidirect |
| 4. #11720142 | C2 | semidirect |
| 5. C22⋊C4×D27 | C2 | semidirect |
| 6. C4×D108 | C2 | semidirect |
| 10. C2×D108 | C4 | semidirect |
| 13. C2×C4×D27 | C22 | semidirect |
| 14. C4⋊C4×C27 | C22 | semidirect |
| 16. C42×C27 | C22 | semidirect |
| 18. (C2×D27)⋊C4 | C22 | semidirect |
| 19. C4⋊Dic27 | C22 | semidirect |
| 20. C4×Dic27 | C22 | semidirect |
| 29. C22×D27 | C2×C4 | semidirect |
| 31. C2×C4×C27 | C2×C4 | semidirect |
| 36. D108 | C2×C4 | semidirect |
| 37. D108 | C2×C4 | semidirect |
| 113. #117 | D27 | semidirect |
| 115. C27 | #518 | semidirect |
| 139. C4⋊C4 | C2×D27 | semidirect |
| 144. C42 | C2×D27 | semidirect |
| 164. C2×C4 | C4×D27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D108 | 2 |
| C27×#117 | 2 |
| #11720175 | 2 |
| #11720142 | 2 |
| C22⋊C4×D27 | 2 |
| C4×D108 | 2 |
| #10589623 | 3 |