Finite Group DatabasebetaFinite Group DatabasebetaOrder 24512.
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×#20259457 | C2 | semidirect |
| 2. #27133872 | C2 | semidirect |
| 3. #27133871 | C2 | semidirect |
| 4. #27133867 | C2 | semidirect |
| 5. #27133866 | C2 | semidirect |
| 6. #27133861 | C2 | semidirect |
| 7. C2×#20259441 | C2 | semidirect |
| 8. C2×#41×C383 | C2 | semidirect |
| 12. #20259457 | C22 | semidirect |
| 13. C2×Dic766 | C22 | semidirect |
| 14. C2×D1532 | C22 | semidirect |
| 17. #20259447 | C22 | semidirect |
| 18. #20259445 | C22 | semidirect |
| 19. #20259444 | C22 | semidirect |
| 20. #20259442 | C22 | semidirect |
| 21. #20259441 | C22 | semidirect |
| 22. #20259441 | C22 | semidirect |
| 23. C2×C383⋊C8 | C22 | semidirect |
| 27. #41×C383 | C22 | semidirect |
| 28. C2×Q8×C383 | C22 | semidirect |
| 30. C2×D4×C383 | C22 | semidirect |
| 81. C383 | #575 | semidirect |
| 84. C2×#41 | D383 | semidirect |
| 98. #41 | C2×D383 | semidirect |
| 100. C2×Q8 | C2×D383 | semidirect |
| 104. C2×D4 | C2×D383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259457 | 2 |
| #27133872 | 2 |
| #27133871 | 2 |
| #27133867 | 2 |
| #27133866 | 2 |
| #27133861 | 2 |
| C2×#20259441 | 2 |
| C2×#41×C383 | 2 |
| #575 | 383 |