Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
462 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #21422698 | C2 | semidirect |
| 5. #21421960 | C2 | semidirect |
| 6. #21421952 | C2 | semidirect |
| 7. C59×#2336 | C2 | semidirect |
| 9. #16837812 | C4 | semidirect |
| 10. #16837768 | C4 | semidirect |
| 193. #2336 | D59 | semidirect |
| 228. C59 | #9382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435286 | 2 |
| #21425014 | 2 |
| #21422698 | 2 |
| #21422642 | 2 |
| #21421960 | 2 |
| #21421952 | 2 |
| C59×#2336 | 2 |
| #9382 | 59 |