Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21437199 | C2 | semidirect |
| 2. #21425832 | C2 | semidirect |
| 3. #21424142 | C2 | semidirect |
| 4. #21422203 | C2 | semidirect |
| 16. C59×#470 | C4 | semidirect |
| 17. C59×#469 | C4 | semidirect |
| 24. #14273667 | D4 | semidirect |
| 150. #470 | Dic59 | semidirect |
| 151. #469 | Dic59 | semidirect |
| 159. C59 | #13077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437199 | 2 |
| #21425832 | 2 |
| #21424142 | 2 |
| #21422203 | 2 |
| C59×#3060 | 2 |
| #13077 | 59 |