Order 20224.
1518 conjugacy classes of subgroups.
The subgroup lattice has 374 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #23764542 | C2 | direct (N × H) |
| 33. C22×Dic158 | Q8 | semidirect |
| 74. C2×Dic158 | C2×Q8 | semidirect |
| 179. C2×C79 | #2024 | semidirect |
| 193. C79 | C2×#2024 | semidirect |
| 365. C2 | #23764542 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579161 | 2 |
| C22×#14579086 | 2 |
| C2×#19098469 | 2 |
| #23764542 | 2 |
| C2×#19098326 | 2 |
| C2×#336×C79 | 2 |
| C2×#2024 | 79 |