Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
516 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 97 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. C22×#14273673 | C2 | semidirect |
| 4. C2×#16837219 | C2 | semidirect |
| 6. #21422189 | C2 | semidirect |
| 7. C2×C59×#362 | C2 | semidirect |
| 187. C2×#362 | D59 | semidirect |
| 216. C59 | #13315 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14273673 | 2 |
| C2×#16837678 | 2 |
| C2×#16837674 | 2 |
| C2×#16837219 | 2 |
| #21425711 | 2 |
| #21422189 | 2 |
| C2×C59×#362 | 2 |
| #13315 | 59 |