Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
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×D349 | C2 | semidirect |
| 2. #26013671 | C2 | semidirect |
| 3. #26013668 | C2 | semidirect |
| 4. #26013666 | C2 | semidirect |
| 5. #26013663 | C2 | semidirect |
| 6. #26013661 | C2 | semidirect |
| 7. #26013659 | C2 | semidirect |
| 8. C2×#19150216 | C2 | semidirect |
| 9. #135×C349 | C2 | semidirect |
| 12. #19150233 | C22 | semidirect |
| 15. Q8×D349 | C22 | semidirect |
| 17. D4×D349 | C22 | semidirect |
| 20. Dic1396 | C22 | semidirect |
| 21. #19150223 | C22 | semidirect |
| 22. #19150222 | C22 | semidirect |
| 23. #19150221 | C22 | semidirect |
| 24. #19150220 | C22 | semidirect |
| 25. D2792 | C22 | semidirect |
| 26. #19150218 | C22 | semidirect |
| 27. #19150216 | C22 | semidirect |
| 28. #19150216 | C22 | semidirect |
| 29. C2×#14584095 | C22 | semidirect |
| 30. #41×C349 | C22 | semidirect |
| 31. Q16×C349 | C22 | semidirect |
| 32. SD16×C349 | C22 | semidirect |
| 33. D8×C349 | C22 | semidirect |
| 34. C2×C8×C349 | C22 | semidirect |
| 75. C349 | #575 | semidirect |
| 84. #135 | D349 | semidirect |
| 91. #41 | C2×D349 | semidirect |
| 99. Q16 | C2×D349 | semidirect |
| 103. SD16 | C2×D349 | semidirect |
| 106. D8 | C2×D349 | semidirect |
| 110. C2×C8 | C2×D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D349 | 2 |
| #26013671 | 2 |
| #26013668 | 2 |
| #26013666 | 2 |
| #26013663 | 2 |
| #26013661 | 2 |
| #26013659 | 2 |
| C2×#19150216 | 2 |
| #135×C349 | 2 |
| #575 | 349 |