Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
554 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 139 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. C4×C8×Dic59 | 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 |
| 74. C4×Dic59 | D8 | semidirect |
| 103. C8×C59 | #104 | semidirect |
| 134. #500 | Dic59 | semidirect |
| 135. #493 | Dic59 | semidirect |
| 136. #486 | Dic59 | semidirect |
| 147. C59 | #9844 | semidirect |
| 233. C8 | #14273654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424925 | 2 |
| C4×C8×Dic59 | 2 |
| #21422855 | 2 |
| #21422547 | 2 |
| C59×#3169 | 2 |
| #9844 | 59 |