Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
414 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21422712 | C2 | semidirect |
| 4. #21422661 | C2 | semidirect |
| 6. #21421978 | C2 | semidirect |
| 7. C59×#1302 | C2 | semidirect |
| 10. #16837811 | C4 | semidirect |
| 11. #16837796 | C4 | semidirect |
| 12. #16837771 | C4 | semidirect |
| 13. #16837762 | C4 | semidirect |
| 198. #1302 | D59 | semidirect |
| 233. C59 | #9431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434805 | 2 |
| #21433085 | 2 |
| #21422712 | 2 |
| #21422661 | 2 |
| #21422635 | 2 |
| #21421978 | 2 |
| C59×#1302 | 2 |
| #9431 | 59 |