Finite Group DatabasebetaFinite Group DatabasebetaOrder 15424.
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. #21440687 | C2 | semidirect |
| 2. #21440668 | C2 | semidirect |
| 3. #21440666 | C2 | semidirect |
| 4. #21440664 | C2 | semidirect |
| 5. #21440661 | C2 | semidirect |
| 6. D8×D241 | C2 | semidirect |
| 7. #21440648 | C2 | semidirect |
| 8. C2×D8×C241 | C2 | semidirect |
| 10. #16838770 | C22 | semidirect |
| 12. #16838769 | C22 | semidirect |
| 15. D4×D241 | C22 | semidirect |
| 16. Dic964 | C22 | semidirect |
| 17. #16838759 | C22 | semidirect |
| 18. #16838758 | C22 | semidirect |
| 19. D1928 | C22 | semidirect |
| 20. #16838755 | C22 | semidirect |
| 21. #16838754 | C22 | semidirect |
| 22. #16838753 | C22 | semidirect |
| 23. C8×D241 | C22 | semidirect |
| 24. C2×D4×C241 | C22 | semidirect |
| 25. D8×C241 | C22 | semidirect |
| 26. D8×C241 | C22 | semidirect |
| 27. C2×C8×C241 | C22 | semidirect |
| 62. C241 | #576 | semidirect |
| 70. C2×D8 | D241 | semidirect |
| 79. C2×D4 | C2×D241 | semidirect |
| 85. D8 | C2×D241 | semidirect |
| 86. D8 | C2×D241 | semidirect |
| 90. C2×C8 | C2×D241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21440687 | 2 |
| #21440668 | 2 |
| #21440666 | 2 |
| #21440664 | 2 |
| #21440661 | 2 |
| D8×D241 | 2 |
| #21440648 | 2 |
| C2×D8×C241 | 2 |
| #576 | 241 |