Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
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. #26015037 | C2 | semidirect |
| 2. #26015018 | C2 | semidirect |
| 3. #26015016 | C2 | semidirect |
| 4. #26015014 | C2 | semidirect |
| 5. #26015011 | C2 | semidirect |
| 6. D8×D353 | C2 | semidirect |
| 7. #26014998 | C2 | semidirect |
| 8. C2×D8×C353 | C2 | semidirect |
| 10. #19150737 | C22 | semidirect |
| 12. #19150736 | C22 | semidirect |
| 15. D4×D353 | C22 | semidirect |
| 16. Dic1412 | C22 | semidirect |
| 17. #19150726 | C22 | semidirect |
| 18. #19150725 | C22 | semidirect |
| 19. D2824 | C22 | semidirect |
| 20. #19150722 | C22 | semidirect |
| 21. #19150721 | C22 | semidirect |
| 22. #19150720 | C22 | semidirect |
| 23. C8×D353 | C22 | semidirect |
| 24. C2×D4×C353 | C22 | semidirect |
| 25. D8×C353 | C22 | semidirect |
| 26. D8×C353 | C22 | semidirect |
| 27. C2×C8×C353 | C22 | semidirect |
| 62. C353 | #576 | semidirect |
| 70. C2×D8 | D353 | semidirect |
| 79. C2×D4 | C2×D353 | semidirect |
| 85. D8 | C2×D353 | semidirect |
| 86. D8 | C2×D353 | semidirect |
| 90. C2×C8 | C2×D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26015037 | 2 |
| #26015018 | 2 |
| #26015016 | 2 |
| #26015014 | 2 |
| #26015011 | 2 |
| D8×D353 | 2 |
| #26014998 | 2 |
| C2×D8×C353 | 2 |
| #576 | 353 |