Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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. #21424142 | C2 | semidirect |
| 3. #21422217 | C2 | semidirect |
| 10. C2×#131×C59 | C4 | semidirect |
| 15. C59×#423 | C4 | semidirect |
| 16. C59×#408 | C4 | semidirect |
| 18. C2×C4×C8×C59 | C4 | semidirect |
| 145. C2×#131 | Dic59 | semidirect |
| 151. #423 | Dic59 | semidirect |
| 153. #408 | Dic59 | semidirect |
| 155. C2×C4×C8 | Dic59 | semidirect |
| 159. C59 | #12807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425761 | 2 |
| #21424142 | 2 |
| #21422217 | 2 |
| C59×#2931 | 2 |
| #12807 | 59 |