Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
1974 conjugacy classes of subgroups.
The subgroup lattice has 314 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21433185 | C2 | semidirect |
| 2. #21433181 | C2 | semidirect |
| 3. #21433177 | C2 | semidirect |
| 4. Q8×#11745664 | C2 | semidirect |
| 7. #16837533 | C22 | semidirect |
| 8. Q8×C59⋊C8 | C22 | semidirect |
| 67. C2×Q8×C59 | M16 | semidirect |
| 183. C59 | #60248 | semidirect |
| 224. C2×Q8 | #11745664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433185 | 2 |
| #21433181 | 2 |
| #21433177 | 2 |
| Q8×#11745664 | 2 |
| #21432729 | 2 |
| C22×C4×Q8×C59 | 2 |
| #60248 | 59 |