Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
642 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 207 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 |
|---|---|---|
| 2. #21433012 | C2 | semidirect |
| 3. #21425981 | C2 | semidirect |
| 4. #21425976 | C2 | semidirect |
| 5. C2×#16837208 | C2 | semidirect |
| 6. #21425695 | C2 | semidirect |
| 7. C59×#2161 | C2 | semidirect |
| 10. #16837845 | C4 | semidirect |
| 11. #16837840 | C4 | semidirect |
| 15. #16837518 | C22 | semidirect |
| 18. #16837208 | C22 | semidirect |
| 19. #16837208 | C22 | semidirect |
| 20. #16837177 | C22 | semidirect |
| 21. C16×Dic59 | C22 | semidirect |
| 24. C59×#368 | C22 | semidirect |
| 121. #2161 | D59 | semidirect |
| 140. #368 | C2×D59 | semidirect |
| 145. C59 | #33464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437232 | 2 |
| #21433012 | 2 |
| #21425981 | 2 |
| #21425976 | 2 |
| C2×#16837208 | 2 |
| #21425695 | 2 |
| C59×#2161 | 2 |
| #33464 | 59 |