Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
468 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 3. #21424230 | C2 | semidirect |
| 4. #21421978 | C2 | semidirect |
| 19. C59×#329 | C4 | semidirect |
| 45. #97×C59 | C2×C4 | semidirect |
| 158. #329 | Dic59 | semidirect |
| 159. C59 | #8914 | semidirect |
| 182. #97 | C2×Dic59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427270 | 2 |
| #21424913 | 2 |
| #21424230 | 2 |
| #21421978 | 2 |
| C2×C59×#329 | 2 |
| #8914 | 59 |