Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
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×C7⋊C8 | C2 | direct (N × H) |
| 3. C2×Q8×C7⋊C8 | C2 | semidirect |
| 4. C2×D4×C7⋊C8 | C2 | semidirect |
| 5. C2×#89697 | C2 | semidirect |
| 6. C22×C4×C7⋊C8 | C2 | semidirect |
| 18. Q8×C7⋊C8 | C22 | semidirect |
| 19. D4×C7⋊C8 | C22 | semidirect |
| 20. #89697 | C22 | semidirect |
| 25. C2×C4×C7⋊C8 | C22 | semidirect |
| 27. C2×C7×#41 | C8 | semidirect |
| 66. C7×#41 | C2×C8 | semidirect |
| 67. C2×C7×Q8 | C2×C8 | semidirect |
| 69. C2×C7×D4 | C2×C8 | semidirect |
| 73. C22×C4×C7 | C2×C8 | semidirect |
| 95. C2×C7⋊C8 | #41 | direct (N × H) |
| 122. C7×Q8 | C22×C8 | semidirect |
| 123. C7×D4 | C22×C8 | semidirect |
| 131. C2×C4×C7 | C22×C8 | semidirect |
| 142. C7⋊C8 | C2×#41 | direct (N × H) |
| 143. C2×#41 | C7⋊C8 | direct (N × H) |
| 191. #41 | C2×C7⋊C8 | direct (N × H) |
| 192. C2×Q8 | C2×C7⋊C8 | semidirect |
| 194. C2×D4 | C2×C7⋊C8 | semidirect |
| 198. C22×C4 | C2×C7⋊C8 | semidirect |
| 224. C2×C7 | C8×#41 | semidirect |
| 233. Q8 | C22×C7⋊C8 | semidirect |
| 234. D4 | C22×C7⋊C8 | semidirect |
| 242. C2×C4 | C22×C7⋊C8 | semidirect |
| 254. C7 | C2×C8×#41 | semidirect |
| 271. C2 | #41×C7⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×#41 | 2 |
| #41×C7⋊C8 | 2 |
| C2×Q8×C7⋊C8 | 2 |
| C2×D4×C7⋊C8 | 2 |
| C2×#89697 | 2 |
| C22×C4×C7⋊C8 | 2 |
| C2×C8×#41 | 7 |