Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
472 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 151 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. #21437237 | C2 | semidirect |
| 2. #21426409 | C2 | semidirect |
| 3. #21426408 | C2 | semidirect |
| 4. #21426403 | C2 | semidirect |
| 5. C2×#16837237 | C2 | semidirect |
| 6. #21426390 | C2 | semidirect |
| 7. C59×#3415 | C2 | semidirect |
| 10. #16837834 | C22 | semidirect |
| 11. C2×D944 | C22 | semidirect |
| 12. #16837242 | C22 | semidirect |
| 13. #16837240 | C22 | semidirect |
| 14. #16837239 | C22 | semidirect |
| 15. #16837237 | C22 | semidirect |
| 16. #16837237 | C22 | semidirect |
| 17. #16837236 | C22 | semidirect |
| 18. C2×C59⋊C32 | C22 | semidirect |
| 21. C59×#508 | C22 | semidirect |
| 22. C2×D16×C59 | C22 | semidirect |
| 94. #3415 | D59 | semidirect |
| 109. #508 | C2×D59 | semidirect |
| 111. C2×D16 | C2×D59 | semidirect |
| 120. C59 | #33982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437237 | 2 |
| #21426409 | 2 |
| #21426408 | 2 |
| #21426403 | 2 |
| C2×#16837237 | 2 |
| #21426390 | 2 |
| C59×#3415 | 2 |
| #33982 | 59 |