Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
396 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 79 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. C22×D108 | C2 | semidirect |
| 2. #11720179 | C2 | semidirect |
| 3. C2×D216 | C2 | semidirect |
| 4. C27×C22⋊C8 | C2 | semidirect |
| 5. #11720061 | C2 | semidirect |
| 13. C2×D108 | C22 | semidirect |
| 14. C2×C8×C27 | C22 | semidirect |
| 16. C4⋊Dic27 | C22 | semidirect |
| 37. D108 | D4 | semidirect |
| 53. C22×C27 | D8 | semidirect |
| 122. C22⋊C8 | D27 | semidirect |
| 123. C27 | #447 | semidirect |
| 154. C2×C8 | C2×D27 | semidirect |
| 203. C22 | D216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D108 | 2 |
| #11720179 | 2 |
| C2×D216 | 2 |
| C27×C22⋊C8 | 2 |
| #11720061 | 2 |
| #10588414 | 3 |