Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
172 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 46 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. #11757431 | C2 | direct (N × H) |
| 3. C23×C27⋊C3 | C3 | semidirect |
| 4. C2×#66353 | C3 | semidirect |
| 9. C22×C27⋊C3 | C2×C3 | semidirect |
| 10. #66353 | C2×C3 | semidirect |
| 23. C2×C27⋊C3 | A4 | semidirect |
| 37. C27⋊C3 | C2×A4 | semidirect |
| 102. C23 | #6869 | semidirect |
| 112. C22 | C2×#6869 | semidirect |
| 118. C2 | #11757431 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757431 | 2 |
| C2×C3×C9×A4 | 3 |
| C23×C27⋊C3 | 3 |
| C2×#66353 | 3 |
| C2×#6869 | 4 |