Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
218 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 125. C59 | #12423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426238 | 2 |
| #21426146 | 2 |
| #21423693 | 2 |
| #21422160 | 2 |
| #21422152 | 2 |
| #21422144 | 2 |
| C8×Q16×C59 | 2 |
| #12423 | 59 |