Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
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×D479 | C2 | semidirect |
| 2. #29506414 | C2 | semidirect |
| 3. #29506411 | C2 | semidirect |
| 4. #29506409 | C2 | semidirect |
| 5. #29506406 | C2 | semidirect |
| 6. #29506404 | C2 | semidirect |
| 7. #29506402 | C2 | semidirect |
| 8. C2×#21440145 | C2 | semidirect |
| 9. #135×C479 | C2 | semidirect |
| 12. #21440162 | C22 | semidirect |
| 15. Q8×D479 | C22 | semidirect |
| 17. D4×D479 | C22 | semidirect |
| 20. Dic1916 | C22 | semidirect |
| 21. #21440152 | C22 | semidirect |
| 22. #21440151 | C22 | semidirect |
| 23. #21440150 | C22 | semidirect |
| 24. #21440149 | C22 | semidirect |
| 25. D3832 | C22 | semidirect |
| 26. #21440147 | C22 | semidirect |
| 27. #21440145 | C22 | semidirect |
| 28. #21440145 | C22 | semidirect |
| 29. C2×C479⋊C8 | C22 | semidirect |
| 30. #41×C479 | C22 | semidirect |
| 31. Q16×C479 | C22 | semidirect |
| 32. SD16×C479 | C22 | semidirect |
| 33. D8×C479 | C22 | semidirect |
| 34. C2×C8×C479 | C22 | semidirect |
| 75. C479 | #575 | semidirect |
| 84. #135 | D479 | semidirect |
| 91. #41 | C2×D479 | semidirect |
| 99. Q16 | C2×D479 | semidirect |
| 103. SD16 | C2×D479 | semidirect |
| 106. D8 | C2×D479 | semidirect |
| 110. C2×C8 | C2×D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D479 | 2 |
| #29506414 | 2 |
| #29506411 | 2 |
| #29506409 | 2 |
| #29506406 | 2 |
| #29506404 | 2 |
| #29506402 | 2 |
| C2×#21440145 | 2 |
| #135×C479 | 2 |
| #575 | 479 |