Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
714 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 267 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. #21424655 | C2 | semidirect |
| 117. C59 | #21913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424655 | 2 |
| #21424167 | 2 |
| #21424080 | 2 |
| C4×C22⋊(C59⋊C8) | 2 |
| C59×#2296 | 2 |
| #21913 | 59 |