Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1328 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 251 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. #21438808 | C2 | semidirect |
| 3. #21432793 | C2 | semidirect |
| 4. #21424512 | C2 | semidirect |
| 5. #21424381 | C2 | semidirect |
| 6. #21423899 | C2 | semidirect |
| 7. C59×#1791 | C2 | semidirect |
| 12. C22×C8×D59 | C22 | semidirect |
| 18. #16837428 | C22 | semidirect |
| 20. #16837365 | C22 | semidirect |
| 21. #16837360 | C22 | semidirect |
| 22. #16837174 | C22 | semidirect |
| 34. C2×#11745664 | D4 | semidirect |
| 37. C22×C59⋊C8 | D4 | semidirect |
| 146. #1791 | D59 | semidirect |
| 170. C59 | #21483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438808 | 2 |
| #21433488 | 2 |
| #21432793 | 2 |
| #21424512 | 2 |
| #21424381 | 2 |
| #21423899 | 2 |
| C59×#1791 | 2 |
| #21483 | 59 |