Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
268 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 124 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. #11757797 | C2 | direct (N × H) |
| 3. C23×C27⋊C3 | C3 | semidirect |
| 4. C2×#66353 | C3 | semidirect |
| 5. C2×C3×C22⋊C27 | C3 | semidirect |
| 6. C2×C27⋊A4 | C3 | semidirect |
| 7. C2×A4×C27 | C3 | semidirect |
| 12. C22×C27⋊C3 | C2×C3 | semidirect |
| 13. #66353 | C2×C3 | semidirect |
| 14. C3×C22⋊C27 | C2×C3 | semidirect |
| 15. C27⋊A4 | C2×C3 | semidirect |
| 16. A4×C27 | C2×C3 | semidirect |
| 32. C2×C27⋊C3 | A4 | semidirect |
| 51. C27⋊C3 | C2×A4 | semidirect |
| 118. C23 | #6903 | semidirect |
| 128. C22 | C2×#6903 | semidirect |
| 134. C2 | #11757797 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757797 | 2 |
| C2×#66436 | 3 |
| C23×C27⋊C3 | 3 |
| C2×#66353 | 3 |
| C2×C3×C22⋊C27 | 3 |
| C2×C27⋊A4 | 3 |
| C2×A4×C27 | 3 |
| C2×#6903 | 4 |