Order 17152.
1674 conjugacy classes of subgroups.
The subgroup lattice has 412 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22573177 | C2 | semidirect |
| 3. #22573142 | C2 | semidirect |
| 101. C2×Q16×C67 | Q8 | semidirect |
| 216. C67 | #61379 | semidirect |
| 259. C2×Q16 | Dic134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574019 | 2 |
| #22573177 | 2 |
| #22573142 | 2 |
| #22570737 | 2 |
| #22570733 | 2 |
| #22570047 | 2 |
| #22570014 | 2 |
| #22569149 | 2 |
| #22569077 | 2 |
| C2×#441×C67 | 2 |
| #61379 | 67 |