Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
634 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 634 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 |
|---|---|---|
| 2. #21424076 | C2 | semidirect |
| 3. #21421916 | C2 | semidirect |
| 4. C59×#1817 | C2 | semidirect |
| 174. #1817 | D59 | semidirect |
| 201. C59 | #7724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432441 | 2 |
| #21424076 | 2 |
| #21421916 | 2 |
| C59×#1817 | 2 |
| #7724 | 59 |