Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
408 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×#16837229 | C2 | semidirect |
| 3. C2×#16837209 | C2 | semidirect |
| 4. C2×#16837187 | C2 | semidirect |
| 5. #21424161 | C2 | semidirect |
| 6. #21422205 | C2 | semidirect |
| 7. C59×#2139 | C2 | semidirect |
| 44. C2×C59⋊C16 | D4 | semidirect |
| 180. #2139 | D59 | semidirect |
| 210. C59 | #13385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433762 | 2 |
| C2×#16837229 | 2 |
| C2×#16837209 | 2 |
| C2×#16837187 | 2 |
| #21424161 | 2 |
| #21422205 | 2 |
| C59×#2139 | 2 |
| #13385 | 59 |