Order 20224.
768 conjugacy classes of subgroups.
The subgroup lattice has 378 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #23761521 | C2 | semidirect |
| 7. #19098537 | C4 | semidirect |
| 10. C2×#14579076 | C4 | semidirect |
| 12. C22×M16×C79 | C4 | semidirect |
| 13. C22×M16×C79 | C4 | semidirect |
| 15. #408×C79 | C4 | semidirect |
| 28. #14579076 | C2×C4 | semidirect |
| 47. C2×M16×C79 | C2×C4 | semidirect |
| 49. C22×C8×C79 | C2×C4 | semidirect |
| 192. C79 | #12577 | semidirect |
| 194. C22×M16 | Dic79 | semidirect |
| 195. C22×M16 | Dic79 | semidirect |
| 204. #408 | Dic79 | semidirect |
| 225. C2×M16 | C2×Dic79 | semidirect |
| 227. C22×C8 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098537 | 2 |
| #23761521 | 2 |
| C79×#2879 | 2 |
| #12577 | 79 |