Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
908 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 165 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. #21432998 | C2 | semidirect |
| 2. #21432795 | C2 | semidirect |
| 3. #21425648 | C2 | semidirect |
| 4. #21425201 | C2 | semidirect |
| 5. #21425163 | C2 | semidirect |
| 6. #21423852 | C2 | semidirect |
| 7. C59×#2091 | C2 | semidirect |
| 45. #14273637 | D4 | semidirect |
| 46. C8×Dic59 | D4 | semidirect |
| 123. #2091 | D59 | semidirect |
| 147. C59 | #23795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432998 | 2 |
| #21432795 | 2 |
| #21425648 | 2 |
| #21425201 | 2 |
| #21425163 | 2 |
| #21423852 | 2 |
| C59×#2091 | 2 |
| #23795 | 59 |