Order 18176.
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. #22589482 | C2 | direct (N × H) |
| 33. C22×Dic142 | Q8 | semidirect |
| 74. C2×Dic142 | C2×Q8 | semidirect |
| 179. C2×C71 | #2024 | semidirect |
| 193. C71 | C2×#2024 | semidirect |
| 365. C2 | #22589482 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556128 | 2 |
| C22×#14556053 | 2 |
| C2×#17985905 | 2 |
| #22589482 | 2 |
| C2×#17985762 | 2 |
| C2×#336×C71 | 2 |
| C2×#2024 | 71 |