Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
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. #21440005 | C2 | semidirect |
| 2. #21439986 | C2 | semidirect |
| 3. #21439984 | C2 | semidirect |
| 4. #21439982 | C2 | semidirect |
| 5. #21439979 | C2 | semidirect |
| 6. D8×D239 | C2 | semidirect |
| 7. #21439966 | C2 | semidirect |
| 8. C2×D8×C239 | C2 | semidirect |
| 10. #16838548 | C22 | semidirect |
| 12. #16838547 | C22 | semidirect |
| 15. D4×D239 | C22 | semidirect |
| 16. Dic956 | C22 | semidirect |
| 17. #16838537 | C22 | semidirect |
| 18. #16838536 | C22 | semidirect |
| 19. D1912 | C22 | semidirect |
| 20. #16838533 | C22 | semidirect |
| 21. #16838532 | C22 | semidirect |
| 22. #16838531 | C22 | semidirect |
| 23. C8×D239 | C22 | semidirect |
| 24. C2×D4×C239 | C22 | semidirect |
| 25. D8×C239 | C22 | semidirect |
| 26. D8×C239 | C22 | semidirect |
| 27. C2×C8×C239 | C22 | semidirect |
| 62. C239 | #576 | semidirect |
| 70. C2×D8 | D239 | semidirect |
| 79. C2×D4 | C2×D239 | semidirect |
| 85. D8 | C2×D239 | semidirect |
| 86. D8 | C2×D239 | semidirect |
| 90. C2×C8 | C2×D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21440005 | 2 |
| #21439986 | 2 |
| #21439984 | 2 |
| #21439982 | 2 |
| #21439979 | 2 |
| D8×D239 | 2 |
| #21439966 | 2 |
| C2×D8×C239 | 2 |
| #576 | 239 |