Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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×#123 | C2 | semidirect |
| 3. #11720185 | C2 | semidirect |
| 4. C4×#6171 | C2 | semidirect |
| 5. #11720145 | C2 | semidirect |
| 6. #11720141 | C2 | semidirect |
| 7. #11720132 | C2 | semidirect |
| 8. C22⋊C4×D27 | C2 | semidirect |
| 9. #11720128 | C2 | semidirect |
| 13. C22×C4×C27 | C22 | semidirect |
| 17. C2×Dic54 | C22 | semidirect |
| 18. C4⋊C4×C27 | C22 | semidirect |
| 20. C22⋊C4×C27 | C22 | semidirect |
| 23. #88372 | C22 | semidirect |
| 27. C4⋊Dic27 | C22 | semidirect |
| 28. Dic27⋊C4 | C22 | semidirect |
| 29. Dic27⋊C4 | C22 | semidirect |
| 30. C4×Dic27 | C22 | semidirect |
| 31. C4×Dic27 | C22 | semidirect |
| 166. #123 | D27 | semidirect |
| 172. C27 | #551 | semidirect |
| 201. C22×C4 | C2×D27 | semidirect |
| 205. C4⋊C4 | C2×D27 | semidirect |
| 213. C22⋊C4 | C2×D27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C27×#123 | 2 |
| #11720186 | 2 |
| #11720185 | 2 |
| C4×#6171 | 2 |
| #11720145 | 2 |
| #11720141 | 2 |
| #11720132 | 2 |
| C22⋊C4×D27 | 2 |
| #11720128 | 2 |
| #10589761 | 3 |