Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
500 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 5. C2×#14273727 | C4 | semidirect |
| 10. #16837267 | C4 | semidirect |
| 13. C4×C4⋊Dic59 | C4 | semidirect |
| 32. #14273642 | Q8 | semidirect |
| 189. C59 | #13299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21429269 | 2 |
| C4×#14273642 | 2 |
| #21422220 | 2 |
| C59×#1799 | 2 |
| #13299 | 59 |