Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
464 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 464 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. #21425788 | C2 | semidirect |
| 3. #21425787 | C2 | semidirect |
| 4. #21425745 | C2 | semidirect |
| 5. #21424144 | C2 | semidirect |
| 6. #21423898 | C2 | semidirect |
| 7. C59×#2122 | C2 | semidirect |
| 8. C22×#11745669 | C4 | semidirect |
| 16. #16837438 | C4 | semidirect |
| 17. #16837407 | C4 | semidirect |
| 18. #16837406 | C4 | semidirect |
| 215. #2122 | D59 | semidirect |
| 248. C59 | #13234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433741 | 2 |
| #21425788 | 2 |
| #21425787 | 2 |
| #21425745 | 2 |
| #21424144 | 2 |
| #21423898 | 2 |
| C59×#2122 | 2 |
| #13234 | 59 |