Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
288 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 130 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. A4×C27⋊C3 | C2 | direct (N × H) |
| 3. C23×C27⋊C3 | C3 | semidirect |
| 4. C2×#66353 | C3 | semidirect |
| 5. C2×C27⋊A4 | C3 | semidirect |
| 6. C2×A4×C27 | C3 | semidirect |
| 11. C22×C27⋊C3 | C2×C3 | semidirect |
| 12. #66353 | C2×C3 | semidirect |
| 13. C27⋊A4 | C2×C3 | semidirect |
| 14. A4×C27 | C2×C3 | semidirect |
| 23. C23×C27 | C32 | semidirect |
| 24. C2×C22⋊C27 | C32 | semidirect |
| 30. C2×C27⋊C3 | A4 | direct (N × H) |
| 43. C22×C27 | C2×C32 | semidirect |
| 44. C22⋊C27 | C2×C32 | semidirect |
| 48. C27⋊C3 | C2×A4 | direct (N × H) |
| 70. C2×C27 | C3×A4 | semidirect |
| 93. C27 | C2×C3×A4 | semidirect |
| 97. C2×A4 | C27⋊C3 | direct (N × H) |
| 119. A4 | C2×C27⋊C3 | direct (N × H) |
| 128. C23 | C3×C27⋊C3 | semidirect |
| 139. C22 | C2×C3×C27⋊C3 | semidirect |
| 146. C2 | A4×C27⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×C27⋊C3 | 2 |
| C2×C3×C9×A4 | 3 |
| C23×C27⋊C3 | 3 |
| C2×#66353 | 3 |
| C2×C27⋊A4 | 3 |
| C2×A4×C27 | 3 |
| C2×C3×C27⋊C3 | 4 |