Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
432 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 15. C22×Q16×C59 | C4 | semidirect |
| 22. C59×#427 | C4 | semidirect |
| 23. C59×#419 | C4 | semidirect |
| 165. C22×Q16 | Dic59 | semidirect |
| 173. #427 | Dic59 | semidirect |
| 174. #419 | Dic59 | semidirect |
| 183. C59 | #13233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425791 | 2 |
| #21425750 | 2 |
| #21424146 | 2 |
| #21423896 | 2 |
| C59×#3059 | 2 |
| #13233 | 59 |