Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
530 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21425014 | C2 | semidirect |
| 3. #21422694 | C2 | semidirect |
| 4. #21422642 | C2 | semidirect |
| 5. #21421960 | C2 | semidirect |
| 6. #21421952 | C2 | semidirect |
| 7. C59×#2337 | C2 | semidirect |
| 9. #16837792 | C4 | semidirect |
| 10. #16837761 | C4 | semidirect |
| 35. #14273727 | C2×C4 | semidirect |
| 36. #14273724 | C2×C4 | semidirect |
| 52. #14273638 | C2×C4 | semidirect |
| 216. #2337 | D59 | semidirect |
| 252. C59 | #9381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435083 | 2 |
| #21425014 | 2 |
| #21422694 | 2 |
| #21422642 | 2 |
| #21421960 | 2 |
| #21421952 | 2 |
| C59×#2337 | 2 |
| #9381 | 59 |