Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2230 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. #11739964 | C2 | direct (N × H) |
| 3. C2×Q8×C7⋊C8 | C2 | semidirect |
| 4. C2×#89784 | C2 | semidirect |
| 5. C2×#89698 | C2 | semidirect |
| 6. C2×C4×#1136 | C2 | semidirect |
| 18. Q8×C7⋊C8 | C22 | semidirect |
| 19. #89784 | C22 | semidirect |
| 20. #89698 | C22 | semidirect |
| 22. C4×#1136 | C22 | semidirect |
| 67. C2×C7×Q8 | M16 | semidirect |
| 95. C2×C7⋊C8 | #41 | semidirect |
| 122. C7×Q8 | C2×M16 | semidirect |
| 142. C7⋊C8 | C2×#41 | semidirect |
| 192. C2×Q8 | #1136 | semidirect |
| 224. C2×C7 | #2971 | semidirect |
| 233. Q8 | C2×#1136 | semidirect |
| 254. C7 | C2×#2971 | semidirect |
| 271. C2 | #11739964 | 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 |
| #11739964 | 2 |
| C2×Q8×C7⋊C8 | 2 |
| C2×#89784 | 2 |
| C2×#89698 | 2 |
| C2×C4×#1136 | 2 |
| C2×#2971 | 7 |