Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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. #21426304 | C2 | semidirect |
| 3. #21426287 | C2 | semidirect |
| 4. #21425882 | C2 | semidirect |
| 5. #21425806 | C2 | semidirect |
| 6. #21425707 | C2 | semidirect |
| 7. C2×C59×#427 | C2 | semidirect |
| 16. #16837229 | C22 | semidirect |
| 17. #16837227 | C22 | semidirect |
| 18. #16837205 | C22 | semidirect |
| 19. #16837202 | C22 | semidirect |
| 140. C2×#427 | D59 | semidirect |
| 170. C59 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433677 | 2 |
| #21426304 | 2 |
| #21426287 | 2 |
| #21425882 | 2 |
| #21425806 | 2 |
| #21425707 | 2 |
| C2×C59×#427 | 2 |
| #33647 | 59 |