Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
660 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 243 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. C2×C42×C27 | C2 | semidirect |
| 4. C2×Dic27⋊C4 | C2 | semidirect |
| 5. C2×C4×Dic27 | C2 | semidirect |
| 6. #11720121 | C2 | direct (N × H) |
| 13. C2×C4×D27 | C4 | semidirect |
| 15. C42×C27 | C22 | semidirect |
| 17. Dic27⋊C4 | C22 | semidirect |
| 18. C4×Dic27 | C22 | semidirect |
| 37. C4×D27 | C2×C4 | semidirect |
| 80. C2×C27 | #117 | semidirect |
| 110. C2×C42 | D27 | semidirect |
| 111. C27 | C2×#117 | semidirect |
| 139. C42 | C2×D27 | semidirect |
| 180. C2 | #11720121 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D27 | 2 |
| C2×C42×C27 | 2 |
| C2×(C2×D27)⋊C4 | 2 |
| C2×Dic27⋊C4 | 2 |
| C2×C4×Dic27 | 2 |
| #11720121 | 2 |
| C2×#63434 | 3 |