Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
434 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 123. C59⋊C8 | #101 | semidirect |
| 167. C59 | #9808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837805 | 2 |
| #21424940 | 2 |
| #21422851 | 2 |
| #21422769 | 2 |
| #21422768 | 2 |
| #21422383 | 2 |
| C59×#1966 | 2 |
| #9808 | 59 |