Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
590 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 147 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. #21424213 | C2 | semidirect |
| 3. C2×#16837147 | C2 | semidirect |
| 5. C59×#1767 | C2 | semidirect |
| 133. #1767 | D59 | semidirect |
| 156. C59 | #9710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432453 | 2 |
| #21424213 | 2 |
| C2×#16837147 | 2 |
| C2×#16837145 | 2 |
| C59×#1767 | 2 |
| #9710 | 59 |