Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 12. #16837124 | C4 | semidirect |
| 13. #16837124 | C4 | semidirect |
| 14. #16837123 | C4 | semidirect |
| 15. C8×C59⋊C8 | C4 | semidirect |
| 120. C59 | #8803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21422399 | 2 |
| #21421969 | 2 |
| #21421967 | 2 |
| #21421962 | 2 |
| #21421961 | 2 |
| C59×#1291 | 2 |
| #8803 | 59 |