Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
498 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21424925 | C2 | semidirect |
| 2. #21423841 | C2 | semidirect |
| 3. #21422855 | C2 | semidirect |
| 4. #21422547 | C2 | semidirect |
| 14. C59×#500 | C4 | semidirect |
| 15. C59×#493 | C4 | semidirect |
| 16. C59×#486 | C4 | semidirect |
| 73. C4×Dic59 | D8 | semidirect |
| 133. #500 | Dic59 | semidirect |
| 134. #493 | Dic59 | semidirect |
| 135. #486 | Dic59 | semidirect |
| 146. C59 | #9847 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424925 | 2 |
| #21423841 | 2 |
| #21422855 | 2 |
| #21422547 | 2 |
| C59×#3169 | 2 |
| #9847 | 59 |