Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
330 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 119 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. C22×Dic866 | C2 | semidirect |
| 3. #28357206 | C2 | direct (N × H) |
| 4. C2×C22⋊Dic433 | C2 | semidirect |
| 5. C2×#20294074 | C2 | semidirect |
| 6. C2×#20294074 | C2 | semidirect |
| 7. C2×C4×Dic433 | C2 | semidirect |
| 8. C2×C22⋊C4×C433 | C2 | semidirect |
| 11. C2×Dic866 | C22 | semidirect |
| 17. C22⋊Dic433 | C22 | semidirect |
| 18. #20294074 | C22 | semidirect |
| 19. #20294074 | C22 | semidirect |
| 20. C4×Dic433 | C22 | semidirect |
| 24. C22⋊C4×C433 | C22 | semidirect |
| 64. C2×C433 | #124 | semidirect |
| 69. C433 | C2×#124 | semidirect |
| 77. C2×C22⋊C4 | D433 | semidirect |
| 93. C22⋊C4 | C2×D433 | semidirect |
| 135. C2 | #28357206 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic866 | 2 |
| C22×C22⋊D433 | 2 |
| #28357206 | 2 |
| C2×C22⋊Dic433 | 2 |
| C2×#20294074 | 2 |
| C2×C4×Dic433 | 2 |
| C2×C22⋊C4×C433 | 2 |
| C2×#124 | 433 |