Finite Group DatabasebetaFinite Group DatabasebetaOrder 31424.
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×D491 | C2 | semidirect |
| 2. #30628369 | C2 | semidirect |
| 3. #30628366 | C2 | semidirect |
| 4. #30628364 | C2 | semidirect |
| 5. #30628361 | C2 | semidirect |
| 6. #30628359 | C2 | semidirect |
| 7. #30628357 | C2 | semidirect |
| 8. C2×#21463311 | C2 | semidirect |
| 9. #135×C491 | C2 | semidirect |
| 12. #21463328 | C22 | semidirect |
| 15. Q8×D491 | C22 | semidirect |
| 17. D4×D491 | C22 | semidirect |
| 20. Dic1964 | C22 | semidirect |
| 21. #21463318 | C22 | semidirect |
| 22. #21463317 | C22 | semidirect |
| 23. #21463316 | C22 | semidirect |
| 24. #21463315 | C22 | semidirect |
| 25. D3928 | C22 | semidirect |
| 26. #21463313 | C22 | semidirect |
| 27. #21463311 | C22 | semidirect |
| 28. #21463311 | C22 | semidirect |
| 29. C2×C491⋊C8 | C22 | semidirect |
| 30. #41×C491 | C22 | semidirect |
| 31. Q16×C491 | C22 | semidirect |
| 32. SD16×C491 | C22 | semidirect |
| 33. D8×C491 | C22 | semidirect |
| 34. C2×C8×C491 | C22 | semidirect |
| 75. C491 | #575 | semidirect |
| 84. #135 | D491 | semidirect |
| 91. #41 | C2×D491 | semidirect |
| 99. Q16 | C2×D491 | semidirect |
| 103. SD16 | C2×D491 | semidirect |
| 106. D8 | C2×D491 | semidirect |
| 110. C2×C8 | C2×D491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D491 | 2 |
| #30628369 | 2 |
| #30628366 | 2 |
| #30628364 | 2 |
| #30628361 | 2 |
| #30628359 | 2 |
| #30628357 | 2 |
| C2×#21463311 | 2 |
| #135×C491 | 2 |
| #575 | 491 |