Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
472 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 127 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. #21437233 | C2 | semidirect |
| 2. #21426409 | C2 | semidirect |
| 3. #21426407 | C2 | semidirect |
| 4. #21426405 | C2 | semidirect |
| 5. #21426402 | C2 | semidirect |
| 6. D32×D59 | C2 | semidirect |
| 7. #21426389 | C2 | semidirect |
| 8. C2×C59×D32 | C2 | semidirect |
| 12. #16837834 | C22 | semidirect |
| 13. #16837831 | C22 | semidirect |
| 14. D16×D59 | C22 | semidirect |
| 16. Dic944 | C22 | semidirect |
| 17. #16837241 | C22 | semidirect |
| 18. #16837240 | C22 | semidirect |
| 19. D1888 | C22 | semidirect |
| 20. #16837237 | C22 | semidirect |
| 21. #16837236 | C22 | semidirect |
| 22. #16837235 | C22 | semidirect |
| 23. C32×D59 | C22 | semidirect |
| 24. C2×D16×C59 | C22 | semidirect |
| 25. C59×D32 | C22 | semidirect |
| 26. C59×D32 | C22 | semidirect |
| 27. C2×C32×C59 | C22 | semidirect |
| 108. C2×D32 | D59 | semidirect |
| 121. C2×D16 | C2×D59 | semidirect |
| 128. D32 | C2×D59 | semidirect |
| 129. D32 | C2×D59 | semidirect |
| 133. C2×C32 | C2×D59 | semidirect |
| 134. C59 | #33982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437233 | 2 |
| #21426409 | 2 |
| #21426407 | 2 |
| #21426405 | 2 |
| #21426402 | 2 |
| D32×D59 | 2 |
| #21426389 | 2 |
| C2×C59×D32 | 2 |
| #33982 | 59 |