Order 15616.
1314 conjugacy classes of subgroups.
The subgroup lattice has 398 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #21461560 | C2 | semidirect |
| 3. #21461545 | C2 | semidirect |
| 4. C4×C22⋊#92420 | C2 | semidirect |
| 7. #16840733 | C4 | semidirect |
| 10. C2×#14519832 | C22 | semidirect |
| 11. C2×C4×#92420 | C22 | semidirect |
| 12. #16840628 | C22 | semidirect |
| 13. #16840628 | C22 | semidirect |
| 25. C2×#11758213 | C2×C4 | semidirect |
| 27. #14519834 | C2×C4 | semidirect |
| 72. C22×C4×C61 | M16 | semidirect |
| 83. C22×Dic61 | M16 | semidirect |
| 221. C61 | #20524 | semidirect |
| 291. C22×C4 | #11758213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840733 | 2 |
| #21461560 | 2 |
| #21461545 | 2 |
| C4×C22⋊#92420 | 2 |
| C2×#16839609 | 2 |
| #20524 | 61 |