Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
490 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21425070 | C2 | semidirect |
| 5. #21421956 | C2 | semidirect |
| 6. #21421926 | C2 | semidirect |
| 7. C59×#1549 | C2 | semidirect |
| 10. #16837776 | C4 | semidirect |
| 11. #16837752 | C4 | semidirect |
| 109. C2×C59⋊C8 | SD16 | semidirect |
| 172. #1549 | D59 | semidirect |
| 201. C59 | #9289 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435021 | 2 |
| #21432813 | 2 |
| #21425070 | 2 |
| #21422657 | 2 |
| #21421956 | 2 |
| #21421926 | 2 |
| C59×#1549 | 2 |
| #9289 | 59 |