Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1132 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1132 conjugacy classes of subgroups — too many to draw. Only its 179 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. #21435011 | C2 | semidirect |
| 2. #21434549 | C2 | semidirect |
| 3. #21423179 | C2 | semidirect |
| 4. #21423150 | C2 | semidirect |
| 5. #21422758 | C2 | semidirect |
| 6. #21422513 | C2 | semidirect |
| 7. C59×#3549 | C2 | semidirect |
| 9. C2×#14273724 | C22 | semidirect |
| 13. #16837776 | C22 | semidirect |
| 15. #16837597 | C22 | semidirect |
| 17. #16837455 | C22 | semidirect |
| 18. C4×#11745664 | C22 | semidirect |
| 19. #16837151 | C22 | semidirect |
| 20. #16837146 | C22 | semidirect |
| 21. D4⋊(C59⋊C8) | C22 | semidirect |
| 24. C59×#555 | C22 | semidirect |
| 26. D42×C59 | C22 | semidirect |
| 174. #3549 | D59 | semidirect |
| 190. #555 | C2×D59 | semidirect |
| 192. D42 | C2×D59 | semidirect |
| 210. C59 | #18714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435011 | 2 |
| #21434549 | 2 |
| #21423179 | 2 |
| #21423150 | 2 |
| #21422758 | 2 |
| #21422513 | 2 |
| C59×#3549 | 2 |
| #18714 | 59 |