Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
630 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 123 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. #21424164 | C2 | semidirect |
| 2. #21421922 | C2 | semidirect |
| 3. #21421917 | C2 | semidirect |
| 174. C59 | #7645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424164 | 2 |
| #21421922 | 2 |
| #21421917 | 2 |
| C59×#2297 | 2 |
| #7645 | 59 |