Order 15104.
3158 conjugacy classes of subgroups.
The subgroup lattice has 344 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #21427014 | C2 | direct (N × H) |
| 10. C2×Q8×Dic59 | C4 | semidirect |
| 36. Q8×Dic59 | C2×C4 | semidirect |
| 65. C2×Q8×C59 | C4⋊C4 | semidirect |
| 113. Q8×C59 | C2×C4⋊C4 | semidirect |
| 172. C2×C59 | #2351 | semidirect |
| 202. C59 | C2×#2351 | semidirect |
| 237. C2×Q8 | Dic59⋊C4 | semidirect |
| 285. Q8 | C2×Dic59⋊C4 | semidirect |
| 335. C2 | #21427014 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×Dic59 | 2 |
| #21427014 | 2 |
| C2×#16837300 | 2 |
| C2×#16837298 | 2 |
| C2×#16837267 | 2 |
| C2×C4×Dic59⋊C4 | 2 |
| C22×C4×Q8×C59 | 2 |
| C2×#2351 | 59 |