Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
930 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 169 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. #21432999 | C2 | semidirect |
| 2. #21432793 | C2 | semidirect |
| 3. #21425649 | C2 | semidirect |
| 4. #21425613 | C2 | semidirect |
| 5. #21425160 | C2 | semidirect |
| 6. #21423852 | C2 | semidirect |
| 7. C59×#2017 | C2 | semidirect |
| 43. #14273637 | D4 | semidirect |
| 44. C8×Dic59 | D4 | semidirect |
| 124. #2017 | D59 | semidirect |
| 147. C59 | #23794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432999 | 2 |
| #21432793 | 2 |
| #21425649 | 2 |
| #21425613 | 2 |
| #21425160 | 2 |
| #21423852 | 2 |
| C59×#2017 | 2 |
| #23794 | 59 |