Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
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. #26013684 | C2 | semidirect |
| 2. #26013665 | C2 | semidirect |
| 3. #26013663 | C2 | semidirect |
| 4. #26013661 | C2 | semidirect |
| 5. #26013658 | C2 | semidirect |
| 6. D8×D349 | C2 | semidirect |
| 7. #26013645 | C2 | semidirect |
| 8. C2×D8×C349 | C2 | semidirect |
| 10. #19150233 | C22 | semidirect |
| 12. #19150232 | C22 | semidirect |
| 15. D4×D349 | C22 | semidirect |
| 16. Dic1396 | C22 | semidirect |
| 17. #19150222 | C22 | semidirect |
| 18. #19150221 | C22 | semidirect |
| 19. D2792 | C22 | semidirect |
| 20. #19150218 | C22 | semidirect |
| 21. #19150217 | C22 | semidirect |
| 22. #19150216 | C22 | semidirect |
| 23. C8×D349 | C22 | semidirect |
| 24. C2×D4×C349 | C22 | semidirect |
| 25. D8×C349 | C22 | semidirect |
| 26. D8×C349 | C22 | semidirect |
| 27. C2×C8×C349 | C22 | semidirect |
| 62. C349 | #576 | semidirect |
| 70. C2×D8 | D349 | semidirect |
| 79. C2×D4 | C2×D349 | semidirect |
| 85. D8 | C2×D349 | semidirect |
| 86. D8 | C2×D349 | semidirect |
| 90. C2×C8 | C2×D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26013684 | 2 |
| #26013665 | 2 |
| #26013663 | 2 |
| #26013661 | 2 |
| #26013658 | 2 |
| D8×D349 | 2 |
| #26013645 | 2 |
| C2×D8×C349 | 2 |
| #576 | 349 |