Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 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. #41×D353 | C2 | semidirect |
| 2. #26015024 | C2 | semidirect |
| 3. #26015021 | C2 | semidirect |
| 4. #26015019 | C2 | semidirect |
| 5. #26015016 | C2 | semidirect |
| 6. #26015014 | C2 | semidirect |
| 7. #26015012 | C2 | semidirect |
| 8. C2×#19150720 | C2 | semidirect |
| 9. #135×C353 | C2 | semidirect |
| 12. #19150737 | C22 | semidirect |
| 15. Q8×D353 | C22 | semidirect |
| 17. D4×D353 | C22 | semidirect |
| 20. Dic1412 | C22 | semidirect |
| 21. #19150727 | C22 | semidirect |
| 22. #19150726 | C22 | semidirect |
| 23. #19150725 | C22 | semidirect |
| 24. #19150724 | C22 | semidirect |
| 25. D2824 | C22 | semidirect |
| 26. #19150722 | C22 | semidirect |
| 27. #19150720 | C22 | semidirect |
| 28. #19150720 | C22 | semidirect |
| 29. C2×#15667725 | C22 | semidirect |
| 30. #41×C353 | C22 | semidirect |
| 31. Q16×C353 | C22 | semidirect |
| 32. SD16×C353 | C22 | semidirect |
| 33. D8×C353 | C22 | semidirect |
| 34. C2×C8×C353 | C22 | semidirect |
| 75. C353 | #575 | semidirect |
| 84. #135 | D353 | semidirect |
| 91. #41 | C2×D353 | semidirect |
| 99. Q16 | C2×D353 | semidirect |
| 103. SD16 | C2×D353 | semidirect |
| 106. D8 | C2×D353 | semidirect |
| 110. C2×C8 | C2×D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D353 | 2 |
| #26015024 | 2 |
| #26015021 | 2 |
| #26015019 | 2 |
| #26015016 | 2 |
| #26015014 | 2 |
| #26015012 | 2 |
| C2×#19150720 | 2 |
| #135×C353 | 2 |
| #575 | 353 |