Order 17152.
1462 conjugacy classes of subgroups.
The subgroup lattice has 348 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22562827 | C2 | semidirect |
| 3. #22560197 | C2 | semidirect |
| 4. #22559942 | C2 | semidirect |
| 14. C2×C4×Q8×C67 | C4 | semidirect |
| 15. C2×C4×D4×C67 | C4 | semidirect |
| 17. C2×#117×C67 | C4 | semidirect |
| 19. C22×C4⋊C4×C67 | C4 | semidirect |
| 68. C2×Q8×C67 | C4⋊C4 | semidirect |
| 73. C2×D4×C67 | C4⋊C4 | semidirect |
| 81. C22×C4×C67 | C4⋊C4 | semidirect |
| 179. C67 | #20634 | semidirect |
| 182. C2×C4×Q8 | Dic67 | semidirect |
| 183. C2×C4×D4 | Dic67 | semidirect |
| 186. C2×#117 | Dic67 | semidirect |
| 188. C22×C4⋊C4 | Dic67 | semidirect |
| 236. C2×Q8 | C4⋊Dic67 | semidirect |
| 241. C2×D4 | C4⋊Dic67 | semidirect |
| 250. C22×C4 | C4⋊Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863370 | 2 |
| #22562827 | 2 |
| #22560197 | 2 |
| #22559942 | 2 |
| C2×#520×C67 | 2 |
| #20634 | 67 |