Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
528 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 141 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. #21423844 | C2 | semidirect |
| 4. #21421978 | C2 | semidirect |
| 17. #16837142 | C4 | semidirect |
| 20. C59×#329 | C4 | semidirect |
| 36. #14273638 | C2×C4 | semidirect |
| 48. #97×C59 | C2×C4 | semidirect |
| 170. #329 | Dic59 | semidirect |
| 171. C59 | #8224 | semidirect |
| 197. #97 | C2×Dic59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #124×Dic59 | 2 |
| #21423844 | 2 |
| C2×#16837142 | 2 |
| #21421978 | 2 |
| C2×C59×#329 | 2 |
| #8224 | 59 |