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. #21426739 | C2 | semidirect |
| 3. #21425015 | C2 | semidirect |
| 4. #21422605 | C2 | semidirect |
| 5. #21421990 | C2 | semidirect |
| 6. #21421951 | C2 | semidirect |
| 7. C59×#1490 | C2 | semidirect |
| 10. #16837692 | C4 | semidirect |
| 11. #16837597 | C4 | semidirect |
| 190. #1490 | D59 | semidirect |
| 221. C59 | #9329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434187 | 2 |
| #21426739 | 2 |
| #21425015 | 2 |
| #21422605 | 2 |
| #21421990 | 2 |
| #21421951 | 2 |
| C59×#1490 | 2 |
| #9329 | 59 |