Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C27×#126 | C2 | semidirect |
| 2. #11720147 | C2 | semidirect |
| 3. C4⋊C4×D27 | C2 | semidirect |
| 5. #11720128 | C2 | semidirect |
| 6. #11720125 | C2 | semidirect |
| 7. C42×D27 | C2 | semidirect |
| 12. C4⋊C4×C27 | C22 | semidirect |
| 14. C42×C27 | C22 | semidirect |
| 18. C4⋊Dic27 | C22 | semidirect |
| 19. Dic27⋊C4 | C22 | semidirect |
| 20. Dic27⋊C4 | C22 | semidirect |
| 21. C4×Dic27 | C22 | semidirect |
| 83. D27 | #126 | direct (N × H) |
| 109. #126 | D27 | direct (N × H) |
| 113. C27 | C2×#126 | semidirect |
| 134. C4⋊C4 | C2×D27 | semidirect |
| 140. C42 | C2×D27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C27×#126 | 2 |
| #11720147 | 2 |
| C4⋊C4×D27 | 2 |
| C22⋊C4×D27 | 2 |
| #11720128 | 2 |
| #11720125 | 2 |
| C42×D27 | 2 |
| D9×#126 | 3 |