Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
418 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 118. C8×C59 | #101 | semidirect |
| 164. C59 | #9806 | semidirect |
| 259. C8 | #14273645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837800 | 2 |
| #21425085 | 2 |
| #21424940 | 2 |
| #21422855 | 2 |
| #21422780 | 2 |
| #21422767 | 2 |
| C59×#1451 | 2 |
| #9806 | 59 |