Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#22575836 | C2 | semidirect |
| 2. #31772659 | C2 | semidirect |
| 3. #31772658 | C2 | semidirect |
| 4. #31772654 | C2 | semidirect |
| 5. #31772653 | C2 | semidirect |
| 6. #31772648 | C2 | semidirect |
| 7. C2×#22575820 | C2 | semidirect |
| 8. C2×#41×C541 | C2 | semidirect |
| 12. #22575836 | C22 | semidirect |
| 13. C2×Dic1082 | C22 | semidirect |
| 14. C2×D2164 | C22 | semidirect |
| 17. #22575826 | C22 | semidirect |
| 18. #22575824 | C22 | semidirect |
| 19. #22575823 | C22 | semidirect |
| 20. #22575821 | C22 | semidirect |
| 21. #22575820 | C22 | semidirect |
| 22. #22575820 | C22 | semidirect |
| 23. C2×#16864513 | C22 | semidirect |
| 27. #41×C541 | C22 | semidirect |
| 28. C2×Q8×C541 | C22 | semidirect |
| 30. C2×D4×C541 | C22 | semidirect |
| 81. C541 | #575 | semidirect |
| 84. C2×#41 | D541 | semidirect |
| 98. #41 | C2×D541 | semidirect |
| 100. C2×Q8 | C2×D541 | semidirect |
| 104. C2×D4 | C2×D541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575836 | 2 |
| #31772659 | 2 |
| #31772658 | 2 |
| #31772654 | 2 |
| #31772653 | 2 |
| #31772648 | 2 |
| C2×#22575820 | 2 |
| C2×#41×C541 | 2 |
| #575 | 541 |