Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
464 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21425787 | C2 | semidirect |
| 3. #21425747 | C2 | semidirect |
| 4. #21423896 | C2 | semidirect |
| 5. C59×#1813 | C2 | semidirect |
| 6. C22×D472 | C4 | semidirect |
| 12. #16837440 | C4 | semidirect |
| 13. #16837408 | C4 | semidirect |
| 164. #1813 | D59 | semidirect |
| 190. C59 | #13234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433744 | 2 |
| #21425787 | 2 |
| #21425747 | 2 |
| #21423896 | 2 |
| C59×#1813 | 2 |
| #13234 | 59 |