Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#20294097 | C2 | semidirect |
| 2. C22×D1732 | C2 | semidirect |
| 3. #28357248 | C2 | direct (N × H) |
| 4. C2×#20294086 | C2 | semidirect |
| 5. C2×D3464 | C2 | semidirect |
| 6. C2×M16×C433 | C2 | semidirect |
| 9. #20294097 | C22 | semidirect |
| 10. C2×Dic866 | C22 | semidirect |
| 14. C2×D1732 | C22 | semidirect |
| 15. C2×D1732 | C22 | semidirect |
| 18. #20294086 | C22 | semidirect |
| 19. D3464 | C22 | semidirect |
| 21. M16×C433 | C22 | semidirect |
| 22. C2×C8×C433 | C22 | semidirect |
| 28. Dic866 | C23 | semidirect |
| 33. D1732 | C23 | semidirect |
| 42. C8×C433 | C23 | semidirect |
| 56. C2×C433 | AGL(1,ℤ/8) | semidirect |
| 60. C433 | C2×AGL(1,ℤ/8) | semidirect |
| 67. C2×M16 | D433 | semidirect |
| 82. M16 | C2×D433 | semidirect |
| 83. C2×C8 | C2×D433 | semidirect |
| 103. C8 | C22×D433 | semidirect |
| 119. C2 | #28357248 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294097 | 2 |
| C22×D1732 | 2 |
| #28357248 | 2 |
| C2×#20294086 | 2 |
| C2×D3464 | 2 |
| C2×M16×C433 | 2 |
| C2×AGL(1,ℤ/8) | 433 |