Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2566 conjugacy classes of subgroups.
The subgroup lattice has 276 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #41×#168 | C2 | direct (N × H) |
| 3. C2×Q8×#168 | C2 | semidirect |
| 4. C2×D4×#168 | C2 | semidirect |
| 5. C2×#65214 | C2 | semidirect |
| 6. C22×C4×#168 | C2 | semidirect |
| 18. Q8×#168 | C22 | semidirect |
| 19. D4×#168 | C22 | semidirect |
| 20. #65214 | C22 | semidirect |
| 25. C2×C4×#168 | C22 | semidirect |
| 27. C2×C5×#41 | C8 | semidirect |
| 66. C5×#41 | C2×C8 | semidirect |
| 67. C2×C5×Q8 | C2×C8 | semidirect |
| 69. C2×C5×D4 | C2×C8 | semidirect |
| 73. C22×C4×C5 | C2×C8 | semidirect |
| 95. C2×#168 | #41 | direct (N × H) |
| 122. C5×Q8 | C22×C8 | semidirect |
| 123. C5×D4 | C22×C8 | semidirect |
| 131. C2×C4×C5 | C22×C8 | semidirect |
| 142. #168 | C2×#41 | direct (N × H) |
| 143. C2×#41 | #168 | direct (N × H) |
| 191. #41 | C2×#168 | direct (N × H) |
| 192. C2×Q8 | C2×#168 | semidirect |
| 194. C2×D4 | C2×#168 | semidirect |
| 198. C22×C4 | C2×#168 | semidirect |
| 224. C2×C5 | C8×#41 | semidirect |
| 233. Q8 | C22×#168 | semidirect |
| 234. D4 | C22×#168 | semidirect |
| 242. C2×C4 | C22×#168 | semidirect |
| 254. C5 | C2×C8×#41 | semidirect |
| 271. C2 | #41×#168 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×#41 | 2 |
| #41×#168 | 2 |
| C2×Q8×#168 | 2 |
| C2×D4×#168 | 2 |
| C2×#65214 | 2 |
| C22×C4×#168 | 2 |
| C2×C8×#41 | 5 |