Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
564 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 125 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. #21434829 | C2 | semidirect |
| 2. #21433006 | C2 | semidirect |
| 3. #21426311 | C2 | semidirect |
| 4. #21426308 | C2 | semidirect |
| 5. #21426265 | C2 | semidirect |
| 6. #21426170 | C2 | semidirect |
| 7. #21426042 | C2 | semidirect |
| 8. #21425995 | C2 | semidirect |
| 9. #21425991 | C2 | semidirect |
| 10. #21425905 | C2 | semidirect |
| 11. C59×#2190 | C2 | semidirect |
| 15. #16837799 | C22 | semidirect |
| 16. #16837777 | C22 | semidirect |
| 24. #16837514 | C22 | semidirect |
| 25. #16837513 | C22 | semidirect |
| 30. #16837225 | C22 | semidirect |
| 31. #16837224 | C22 | semidirect |
| 32. #16837222 | C22 | semidirect |
| 33. #16837216 | C22 | semidirect |
| 34. #16837215 | C22 | semidirect |
| 37. #16837179 | C22 | semidirect |
| 111. Q16×C59 | #41 | semidirect |
| 116. D8×C59 | #41 | semidirect |
| 209. #2190 | D59 | semidirect |
| 250. C59 | #33688 | semidirect |
| 319. Q16 | #11745687 | semidirect |
| 326. D8 | #11745687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434829 | 2 |
| #21433006 | 2 |
| #21426311 | 2 |
| #21426308 | 2 |
| #21426265 | 2 |
| #21426170 | 2 |
| #21426042 | 2 |
| #21425995 | 2 |
| #21425991 | 2 |
| #21425905 | 2 |
| C59×#2190 | 2 |
| #33688 | 59 |