Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
464 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21426306 | C2 | semidirect |
| 3. #21426300 | C2 | semidirect |
| 4. #21426257 | C2 | semidirect |
| 5. #21426205 | C2 | semidirect |
| 6. C4×Dic472 | C2 | semidirect |
| 8. #21425883 | C2 | semidirect |
| 9. C59×#2253 | C2 | semidirect |
| 130. #2253 | D59 | semidirect |
| 167. C59 | #33919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21436463 | 2 |
| #21426306 | 2 |
| #21426300 | 2 |
| #21426257 | 2 |
| #21426205 | 2 |
| C4×Dic472 | 2 |
| #21425929 | 2 |
| #21425883 | 2 |
| C59×#2253 | 2 |
| #33919 | 59 |