Order 1792.
650 conjugacy classes of subgroups.
The subgroup lattice has 368 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11725471 | C2 | semidirect |
| 9. C4×C7×M16 | C4 | semidirect |
| 11. C2×C7×#97 | C4 | semidirect |
| 23. #89698 | C4 | semidirect |
| 25. C2×C4⋊(C7⋊C8) | C4 | semidirect |
| 127. C4×M16 | Dic7 | semidirect |
| 130. C2×#97 | Dic7 | semidirect |
| 336. C7 | #8073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×M16 | 2 |
| #11739505 | 2 |
| C2×#89698 | 2 |
| #11725471 | 2 |
| #8073 | 7 |