Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
162 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 3. #28357283 | C2 | direct (N × H) |
| 12. C2×Dic866 | C4 | semidirect |
| 15. Q8×D433 | C4 | semidirect |
| 19. C2×Q8×C433 | C4 | semidirect |
| 27. Dic866 | C2×C4 | semidirect |
| 37. Q8×C433 | C2×C4 | semidirect |
| 52. C2×C433 | #103 | semidirect |
| 54. D433 | #103 | semidirect |
| 57. C433 | C2×#103 | semidirect |
| 69. C2×Q8 | #13181884 | semidirect |
| 84. Q8 | C2×#13181884 | semidirect |
| 113. C2 | #28357283 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294105 | 2 |
| C2×C4⋊#13181884 | 2 |
| #28357283 | 2 |
| C2×Q8×D433 | 2 |
| C2×#103 | 433 |