Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
820 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 1. #21424929 | C2 | semidirect |
| 2. #21422818 | C2 | semidirect |
| 3. #21422731 | C2 | semidirect |
| 4. #21422604 | C2 | semidirect |
| 6. #16837459 | C22 | semidirect |
| 7. #16837426 | C22 | semidirect |
| 9. #16837248 | C22 | semidirect |
| 16. C59×#555 | C4 | semidirect |
| 18. D42×C59 | C4 | semidirect |
| 162. #555 | Dic59 | semidirect |
| 164. D42 | Dic59 | semidirect |
| 177. C59 | #8491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424929 | 2 |
| #21422818 | 2 |
| #21422731 | 2 |
| #21422604 | 2 |
| C59×#3549 | 2 |
| #8491 | 59 |