Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
468 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. #21425768 | C2 | semidirect |
| 3. #21425767 | C2 | semidirect |
| 4. #21425747 | C2 | semidirect |
| 5. #21424140 | C2 | semidirect |
| 6. #21423899 | C2 | semidirect |
| 7. C59×#2122 | C2 | semidirect |
| 8. C22×#11745669 | C4 | semidirect |
| 16. #16837438 | C4 | semidirect |
| 17. #16837407 | C4 | semidirect |
| 18. #16837406 | C4 | semidirect |
| 217. #2122 | D59 | semidirect |
| 250. C59 | #13231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433741 | 2 |
| #21425768 | 2 |
| #21425767 | 2 |
| #21425747 | 2 |
| #21424140 | 2 |
| #21423899 | 2 |
| C59×#2122 | 2 |
| #13231 | 59 |