Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
512 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 512 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. #21434750 | C2 | semidirect |
| 3. #21426316 | C2 | semidirect |
| 4. #21426313 | C2 | semidirect |
| 5. #21426270 | C2 | semidirect |
| 6. #21426175 | C2 | semidirect |
| 8. #21425988 | C2 | semidirect |
| 9. #21425984 | C2 | semidirect |
| 10. #21425909 | C2 | semidirect |
| 15. #16837802 | C22 | semidirect |
| 16. #16837780 | C22 | semidirect |
| 24. #16837509 | C22 | semidirect |
| 25. #16837508 | C22 | semidirect |
| 30. #16837225 | C22 | semidirect |
| 31. #16837224 | C22 | semidirect |
| 32. #16837222 | C22 | semidirect |
| 33. #16837219 | C22 | semidirect |
| 34. #16837218 | C22 | semidirect |
| 37. #16837179 | C22 | semidirect |
| 240. C59 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434750 | 2 |
| #21432999 | 2 |
| #21426316 | 2 |
| #21426313 | 2 |
| #21426270 | 2 |
| #21426175 | 2 |
| #21426047 | 2 |
| #21425988 | 2 |
| #21425984 | 2 |
| #21425909 | 2 |
| C59×#2191 | 2 |
| #33693 | 59 |