Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
468 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21424231 | C2 | semidirect |
| 4. #21421978 | C2 | semidirect |
| 14. #16837142 | C4 | semidirect |
| 29. #14273638 | C2×C4 | semidirect |
| 159. C59 | #8914 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427270 | 2 |
| #21424231 | 2 |
| C2×#16837142 | 2 |
| #21421978 | 2 |
| C59×#1959 | 2 |
| #8914 | 59 |