Finite Group DatabasebetaFinite Group Databasebeta← C2×C3⋊((C27⋊C3)⋊C4) #14517683
Order 1944.
304 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 126 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. C3⋊((C27⋊C3)⋊C4) | C2 | direct (N × H) |
| 4. C2×C3⋊Dic27 | C3 | semidirect |
| 6. C2×C3×C27⋊C3 | C4 | semidirect |
| 14. C3⋊Dic27 | C2×C3 | semidirect |
| 16. C3×C27⋊C3 | C2×C4 | semidirect |
| 26. C2×C27⋊C3 | Dic3 | semidirect |
| 30. C2×C3×C27 | C3×C4 | semidirect |
| 48. C27⋊C3 | C2×Dic3 | semidirect |
| 50. C3×C27 | C2×C3×C4 | semidirect |
| 72. C2×C27 | C3×Dic3 | semidirect |
| 95. C27 | C2×C3×Dic3 | semidirect |
| 135. C2×C3 | (C27⋊C3)⋊C4 | semidirect |
| 143. C3 | C2×(C27⋊C3)⋊C4 | semidirect |
| 145. C2 | C3⋊((C27⋊C3)⋊C4) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C27⋊C3 | 2 |
| C3⋊((C27⋊C3)⋊C4) | 2 |
| C2×C3×C3⋊Dic9 | 3 |
| C2×C3⋊Dic27 | 3 |
| C2×(C27⋊C3)⋊C4 | 3 |