Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
406 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21425868 | C2 | semidirect |
| 3. #21425811 | C2 | semidirect |
| 4. #21425811 | C2 | semidirect |
| 5. #21425724 | C2 | semidirect |
| 6. #21422212 | C2 | semidirect |
| 7. C59×#1812 | C2 | semidirect |
| 164. #1812 | D59 | semidirect |
| 189. C59 | #13404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837672 | 2 |
| #21425868 | 2 |
| #21425811 | 2 |
| #21425724 | 2 |
| #21422212 | 2 |
| C59×#1812 | 2 |
| #13404 | 59 |