Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
316 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 22. #14273667 | Q8 | semidirect |
| 120. C59 | #13270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425862 | 2 |
| #21425701 | 2 |
| #21422182 | 2 |
| #21422178 | 2 |
| C59×#2960 | 2 |
| #13270 | 59 |