Finite Group DatabasebetaFinite Group DatabasebetaOrder 26816.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #27211711 | C2 | semidirect |
| 2. #27211711 | C2 | semidirect |
| 3. #27211704 | C2 | semidirect |
| 4. #27211702 | C2 | semidirect |
| 5. #27211701 | C2 | semidirect |
| 6. #27211700 | C2 | semidirect |
| 7. #27211697 | C2 | semidirect |
| 8. #27211695 | C2 | semidirect |
| 10. C4×C22⋊D419 | C2 | semidirect |
| 11. (C22⋊D419)⋊C4 | C2 | semidirect |
| 12. #27211677 | C2 | semidirect |
| 13. #27211674 | C2 | semidirect |
| 14. C2×C22⋊Dic419 | C2 | semidirect |
| 15. C2×C22⋊C4×C419 | C2 | semidirect |
| 16. C2×Dic838 | C22 | semidirect |
| 22. C2×C4×D419 | C22 | semidirect |
| 23. C4⋊Dic419 | C22 | semidirect |
| 24. C4⋊Dic419 | C22 | semidirect |
| 25. C4⋊Dic419 | C22 | semidirect |
| 26. Dic419⋊C4 | C22 | semidirect |
| 27. Dic419⋊C4 | C22 | semidirect |
| 28. Dic419⋊C4 | C22 | semidirect |
| 29. Dic419⋊C4 | C22 | semidirect |
| 30. Dic419⋊C4 | C22 | semidirect |
| 38. (C2×D419)⋊C4 | C22 | semidirect |
| 39. (C2×D419)⋊C4 | C22 | semidirect |
| 40. (C2×D419)⋊C4 | C22 | semidirect |
| 41. C4×Dic419 | C22 | semidirect |
| 42. C4×Dic419 | C22 | semidirect |
| 43. C4×Dic419 | C22 | semidirect |
| 110. C419 | #551 | semidirect |
| 126. C2×C22⋊C4 | D419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27211711 | 2 |
| #27211704 | 2 |
| #27211702 | 2 |
| #27211701 | 2 |
| #27211700 | 2 |
| #27211697 | 2 |
| #27211695 | 2 |
| #27211687 | 2 |
| C4×C22⋊D419 | 2 |
| (C22⋊D419)⋊C4 | 2 |
| #27211677 | 2 |
| #27211674 | 2 |
| C2×C22⋊Dic419 | 2 |
| C2×C22⋊C4×C419 | 2 |
| #551 | 419 |