Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
422 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 87 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. #21425870 | C2 | semidirect |
| 3. #21425824 | C2 | semidirect |
| 4. #21425706 | C2 | semidirect |
| 5. #21424131 | C2 | semidirect |
| 6. #21422211 | C2 | semidirect |
| 7. C59×#2148 | C2 | semidirect |
| 44. C2×C59⋊C16 | D4 | semidirect |
| 178. #2148 | D59 | semidirect |
| 208. C59 | #13395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433673 | 2 |
| #21425870 | 2 |
| #21425824 | 2 |
| #21425706 | 2 |
| #21424131 | 2 |
| #21422211 | 2 |
| C59×#2148 | 2 |
| #13395 | 59 |