Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
690 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 119 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. #21426694 | C2 | semidirect |
| 2. #21422664 | C2 | semidirect |
| 3. C2×#16837126 | C2 | semidirect |
| 4. #21421963 | C2 | semidirect |
| 16. C59×#397 | C4 | semidirect |
| 18. C59×#392 | C4 | semidirect |
| 30. C59⋊#95 | D4 | semidirect |
| 197. #397 | Dic59 | semidirect |
| 199. #392 | Dic59 | semidirect |
| 208. C59 | #9205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426694 | 2 |
| #21422664 | 2 |
| C2×#16837126 | 2 |
| #21421963 | 2 |
| C59×#2617 | 2 |
| #9205 | 59 |