Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 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. #27212411 | C2 | semidirect |
| 2. #27212392 | C2 | semidirect |
| 3. #27212390 | C2 | semidirect |
| 4. #27212388 | C2 | semidirect |
| 5. #27212385 | C2 | semidirect |
| 6. D8×D421 | C2 | semidirect |
| 7. #27212372 | C2 | semidirect |
| 8. C2×D8×C421 | C2 | semidirect |
| 10. #20269771 | C22 | semidirect |
| 12. #20269770 | C22 | semidirect |
| 15. D4×D421 | C22 | semidirect |
| 16. Dic1684 | C22 | semidirect |
| 17. #20269760 | C22 | semidirect |
| 18. #20269759 | C22 | semidirect |
| 19. D3368 | C22 | semidirect |
| 20. #20269756 | C22 | semidirect |
| 21. #20269755 | C22 | semidirect |
| 22. #20269754 | C22 | semidirect |
| 23. C8×D421 | C22 | semidirect |
| 24. C2×D4×C421 | C22 | semidirect |
| 25. D8×C421 | C22 | semidirect |
| 26. D8×C421 | C22 | semidirect |
| 27. C2×C8×C421 | C22 | semidirect |
| 62. C421 | #576 | semidirect |
| 70. C2×D8 | D421 | semidirect |
| 79. C2×D4 | C2×D421 | semidirect |
| 85. D8 | C2×D421 | semidirect |
| 86. D8 | C2×D421 | semidirect |
| 90. C2×C8 | C2×D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27212411 | 2 |
| #27212392 | 2 |
| #27212390 | 2 |
| #27212388 | 2 |
| #27212385 | 2 |
| D8×D421 | 2 |
| #27212372 | 2 |
| C2×D8×C421 | 2 |
| #576 | 421 |