Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
766 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #21424894 | C2 | semidirect |
| 3. #21422797 | C2 | semidirect |
| 4. #21422791 | C2 | semidirect |
| 5. #21422710 | C2 | semidirect |
| 6. #21422436 | C2 | semidirect |
| 7. C59×#1530 | C2 | semidirect |
| 222. #1530 | D59 | semidirect |
| 255. C59 | #8458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21437945 | 2 |
| #21424894 | 2 |
| #21422797 | 2 |
| #21422791 | 2 |
| #21422710 | 2 |
| #21422436 | 2 |
| C59×#1530 | 2 |
| #8458 | 59 |