Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
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. #31772673 | C2 | semidirect |
| 2. #31772654 | C2 | semidirect |
| 3. #31772652 | C2 | semidirect |
| 4. #31772650 | C2 | semidirect |
| 5. #31772647 | C2 | semidirect |
| 6. D8×D541 | C2 | semidirect |
| 7. #31772634 | C2 | semidirect |
| 8. C2×D8×C541 | C2 | semidirect |
| 10. #22575836 | C22 | semidirect |
| 12. #22575835 | C22 | semidirect |
| 15. D4×D541 | C22 | semidirect |
| 16. Dic2164 | C22 | semidirect |
| 17. #22575825 | C22 | semidirect |
| 18. #22575824 | C22 | semidirect |
| 19. D4328 | C22 | semidirect |
| 20. #22575821 | C22 | semidirect |
| 21. #22575820 | C22 | semidirect |
| 22. #22575819 | C22 | semidirect |
| 23. C8×D541 | C22 | semidirect |
| 24. C2×D4×C541 | C22 | semidirect |
| 25. D8×C541 | C22 | semidirect |
| 26. D8×C541 | C22 | semidirect |
| 27. C2×C8×C541 | C22 | semidirect |
| 62. C541 | #576 | semidirect |
| 70. C2×D8 | D541 | semidirect |
| 79. C2×D4 | C2×D541 | semidirect |
| 85. D8 | C2×D541 | semidirect |
| 86. D8 | C2×D541 | semidirect |
| 90. C2×C8 | C2×D541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31772673 | 2 |
| #31772654 | 2 |
| #31772652 | 2 |
| #31772650 | 2 |
| #31772647 | 2 |
| D8×D541 | 2 |
| #31772634 | 2 |
| C2×D8×C541 | 2 |
| #576 | 541 |