Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
296 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 136 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. C3×C27⋊A4 | C2 | direct (N × H) |
| 3. C23×C3×C27 | C3 | semidirect |
| 4. C2×C3×C22⋊C27 | C3 | semidirect |
| 5. C2×C27⋊A4 | C3 | direct (N × H) |
| 10. C22×C3×C27 | C2×C3 | semidirect |
| 11. C3×C22⋊C27 | C2×C3 | semidirect |
| 12. C27⋊A4 | C2×C3 | direct (N × H) |
| 19. C23×C27 | C32 | semidirect |
| 20. C2×C22⋊C27 | C32 | semidirect |
| 26. C2×C3×C27 | A4 | semidirect |
| 36. C22×C27 | C2×C32 | semidirect |
| 37. C22⋊C27 | C2×C32 | semidirect |
| 41. C3×C27 | C2×A4 | semidirect |
| 58. C2×C27 | C3×A4 | semidirect |
| 77. C27 | C2×C3×A4 | semidirect |
| 78. C23×C3 | C27⋊C3 | semidirect |
| 97. C22×C3 | C2×C27⋊C3 | semidirect |
| 106. C23 | C3×C27⋊C3 | semidirect |
| 112. C2×C3 | C27⋊A4 | direct (N × H) |
| 116. C22 | C2×C3×C27⋊C3 | semidirect |
| 118. C3 | C2×C27⋊A4 | direct (N × H) |
| 122. C2 | C3×C27⋊A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C27⋊A4 | 2 |
| C2×C3×C9×A4 | 3 |
| C23×C3×C27 | 3 |
| C2×C3×C22⋊C27 | 3 |
| C2×C27⋊A4 | 3 |
| C2×C3×C27⋊C3 | 4 |