Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
338 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 21. C59×#333 | C4 | semidirect |
| 22. C59×#332 | C4 | semidirect |
| 158. #333 | Dic59 | semidirect |
| 159. #332 | Dic59 | semidirect |
| 161. C59 | #9579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425074 | 2 |
| C4⋊C8×Dic59 | 2 |
| #21422867 | 2 |
| #21422499 | 2 |
| #21421993 | 2 |
| #21421928 | 2 |
| C59×#1542 | 2 |
| #9579 | 59 |