Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
566 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×#16837216 | C2 | semidirect |
| 3. #21425813 | C2 | semidirect |
| 4. #21423975 | C2 | semidirect |
| 5. C2×C59×#364 | C2 | semidirect |
| 10. #16837779 | C4 | semidirect |
| 37. #14273663 | D4 | semidirect |
| 38. #14273661 | D4 | semidirect |
| 128. C2×#364 | D59 | semidirect |
| 151. C59 | #13261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837779 | 2 |
| C2×#16837216 | 2 |
| #21425813 | 2 |
| #21423975 | 2 |
| C2×C59×#364 | 2 |
| #13261 | 59 |