Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
184 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 70 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×C3×Dic27 | C2 | semidirect |
| 4. #88372 | C3 | direct (N × H) |
| 6. C22×C3×C27 | C4 | semidirect |
| 13. C2×Dic27 | C2×C3 | semidirect |
| 27. C22×C27 | C3×C4 | semidirect |
| 30. C3×C27 | C22⋊C4 | semidirect |
| 60. C27 | C3×C22⋊C4 | semidirect |
| 81. C22×C3 | Dic27 | semidirect |
| 102. C22 | C3×Dic27 | semidirect |
| 106. C3 | #88372 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C27 | 2 |
| C2×C3×Dic27 | 2 |
| C3×#3676 | 3 |
| #88372 | 3 |