Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
2830 conjugacy classes of subgroups.
The subgroup lattice has 280 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #21432660 | C2 | direct (N × H) |
| 3. C2×#16837429 | C2 | semidirect |
| 4. C2×#16837426 | C2 | semidirect |
| 11. #16837429 | C22 | semidirect |
| 12. #16837426 | C22 | semidirect |
| 13. C2×C4⋊(C59⋊C8) | C22 | semidirect |
| 30. C4⋊(C59⋊C8) | C23 | semidirect |
| 142. C2×C59 | #2905 | semidirect |
| 161. C59 | C2×#2905 | semidirect |
| 276. C2 | #21432660 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11745664 | 2 |
| #21432660 | 2 |
| C2×#16837429 | 2 |
| C2×#16837426 | 2 |
| C22×#117×C59 | 2 |
| C2×#2905 | 59 |