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. #27212412 | C2 | semidirect |
| 2. #27212393 | C2 | semidirect |
| 3. #27212391 | C2 | semidirect |
| 4. #27212389 | C2 | semidirect |
| 5. C2×D3368 | C2 | semidirect |
| 6. D8×D421 | C2 | semidirect |
| 7. #27212372 | C2 | semidirect |
| 8. #135×C421 | C2 | semidirect |
| 9. #20269772 | C22 | semidirect |
| 13. C2×D1684 | C22 | semidirect |
| 15. D4×D421 | C22 | semidirect |
| 16. #20269758 | C22 | semidirect |
| 17. D3368 | C22 | semidirect |
| 18. D3368 | C22 | semidirect |
| 19. #20269756 | C22 | semidirect |
| 20. #20269755 | C22 | semidirect |
| 21. #20269754 | C22 | semidirect |
| 22. C8×D421 | C22 | semidirect |
| 23. #41×C421 | C22 | semidirect |
| 24. Q16×C421 | C22 | semidirect |
| 25. SD16×C421 | C22 | semidirect |
| 26. D8×C421 | C22 | semidirect |
| 27. C2×C8×C421 | C22 | semidirect |
| 62. C421 | #576 | semidirect |
| 68. #135 | D421 | semidirect |
| 75. #41 | C2×D421 | semidirect |
| 80. Q16 | C2×D421 | semidirect |
| 82. SD16 | 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 |
|---|---|
| #27212412 | 2 |
| #27212393 | 2 |
| #27212391 | 2 |
| #27212389 | 2 |
| C2×D3368 | 2 |
| D8×D421 | 2 |
| #27212372 | 2 |
| #135×C421 | 2 |
| #576 | 421 |