Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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. #21426310 | C2 | semidirect |
| 3. #21425870 | C2 | semidirect |
| 4. C2×#16837214 | C2 | semidirect |
| 5. #21425717 | C2 | semidirect |
| 6. C59×#2916 | C2 | semidirect |
| 14. #16837226 | C22 | semidirect |
| 16. #16837184 | C22 | semidirect |
| 20. C59×#430 | C22 | semidirect |
| 127. #2916 | D59 | semidirect |
| 145. #430 | C2×D59 | semidirect |
| 153. C59 | #33657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433744 | 2 |
| #21426310 | 2 |
| #21425870 | 2 |
| C2×#16837214 | 2 |
| #21425717 | 2 |
| C59×#2916 | 2 |
| #33657 | 59 |