Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
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. #27212359 | C2 | semidirect |
| 2. #27212359 | C2 | semidirect |
| 3. #27212352 | C2 | semidirect |
| 4. #27212350 | C2 | semidirect |
| 5. #27212349 | C2 | semidirect |
| 6. #27212348 | C2 | semidirect |
| 7. #27212345 | C2 | semidirect |
| 8. #27212343 | C2 | semidirect |
| 10. C4×C22⋊D421 | C2 | semidirect |
| 11. #27212326 | C2 | semidirect |
| 12. #27212325 | C2 | semidirect |
| 13. #27212322 | C2 | semidirect |
| 14. C2×C22⋊Dic421 | C2 | semidirect |
| 15. C2×C22⋊C4×C421 | C2 | semidirect |
| 16. C2×Dic842 | C22 | semidirect |
| 22. C2×C4×D421 | C22 | semidirect |
| 23. C4⋊Dic421 | C22 | semidirect |
| 24. C4⋊Dic421 | C22 | semidirect |
| 25. C4⋊Dic421 | C22 | semidirect |
| 26. #20269750 | C22 | semidirect |
| 27. #20269750 | C22 | semidirect |
| 28. #20269750 | C22 | semidirect |
| 29. #20269750 | C22 | semidirect |
| 30. #20269750 | C22 | semidirect |
| 38. #20269748 | C22 | semidirect |
| 39. #20269748 | C22 | semidirect |
| 40. #20269748 | C22 | semidirect |
| 41. C4×Dic421 | C22 | semidirect |
| 42. C4×Dic421 | C22 | semidirect |
| 43. C4×Dic421 | C22 | semidirect |
| 110. C421 | #551 | semidirect |
| 126. C2×C22⋊C4 | D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27212359 | 2 |
| #27212352 | 2 |
| #27212350 | 2 |
| #27212349 | 2 |
| #27212348 | 2 |
| #27212345 | 2 |
| #27212343 | 2 |
| #27212335 | 2 |
| C4×C22⋊D421 | 2 |
| #27212326 | 2 |
| #27212325 | 2 |
| #27212322 | 2 |
| C2×C22⋊Dic421 | 2 |
| C2×C22⋊C4×C421 | 2 |
| #551 | 421 |