Order 17152.
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. #22561351 | C2 | direct (N × H) |
| 33. C22×Dic134 | Q8 | semidirect |
| 74. C2×Dic134 | C2×Q8 | semidirect |
| 179. C2×C67 | #2024 | semidirect |
| 193. C67 | C2×#2024 | semidirect |
| 365. C2 | #22561351 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14524043 | 2 |
| C22×#14523968 | 2 |
| C2×#16863302 | 2 |
| #22561351 | 2 |
| C2×#16863159 | 2 |
| C2×#336×C67 | 2 |
| C2×#2024 | 67 |