Order 20224.
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. #23766318 | C2 | direct (N × H) |
| 10. C2×Q8×Dic79 | C4 | semidirect |
| 36. Q8×Dic79 | C2×C4 | semidirect |
| 87. C2×Q8×C79 | C4⋊C4 | semidirect |
| 113. Q8×C79 | C2×C4⋊C4 | semidirect |
| 164. C2×C79 | #2351 | semidirect |
| 180. C79 | C2×#2351 | semidirect |
| 237. C2×Q8 | Dic79⋊C4 | semidirect |
| 285. Q8 | C2×Dic79⋊C4 | semidirect |
| 335. C2 | #23766318 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×Dic79 | 2 |
| #23766318 | 2 |
| C2×#19098461 | 2 |
| C2×#19098459 | 2 |
| C2×#19098428 | 2 |
| C2×C4×Dic79⋊C4 | 2 |
| C22×C4×Q8×C79 | 2 |
| C2×#2351 | 79 |