Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
716 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #21424031 | C2 | semidirect |
| 5. #21421964 | C2 | semidirect |
| 6. #21421963 | C2 | semidirect |
| 7. C59×#1787 | C2 | semidirect |
| 17. #16837321 | C4 | semidirect |
| 18. #16837313 | C4 | semidirect |
| 237. #1787 | D59 | semidirect |
| 271. C59 | #9471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433122 | 2 |
| #21427455 | 2 |
| #21424081 | 2 |
| #21424031 | 2 |
| #21421964 | 2 |
| #21421963 | 2 |
| C59×#1787 | 2 |
| #9471 | 59 |