Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
414 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 1. #21425869 | C2 | semidirect |
| 2. #21425824 | C2 | semidirect |
| 3. #21425812 | C2 | semidirect |
| 4. #21425700 | C2 | semidirect |
| 5. #21425007 | C2 | semidirect |
| 6. #21424995 | C2 | semidirect |
| 24. C2×SD32×C59 | C4 | semidirect |
| 25. C2×D16×C59 | C4 | semidirect |
| 179. C2×SD32 | Dic59 | semidirect |
| 180. C2×D16 | Dic59 | semidirect |
| 194. C59 | #13247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425869 | 2 |
| #21425824 | 2 |
| #21425812 | 2 |
| #21425700 | 2 |
| #21425007 | 2 |
| #21424995 | 2 |
| C2×C59×#509 | 2 |
| #13247 | 59 |