Order 1792.
684 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. #11725542 | C2 | semidirect |
| 8. C7×#432 | C4 | semidirect |
| 11. C7×#423 | C4 | semidirect |
| 23. #89697 | C4 | semidirect |
| 25. C2×C4⋊(C7⋊C8) | C4 | semidirect |
| 120. #432 | Dic7 | semidirect |
| 127. #423 | Dic7 | semidirect |
| 336. C7 | #7870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2920 | 2 |
| C4×#6489 | 2 |
| C2×#89697 | 2 |
| #11725542 | 2 |
| #7870 | 7 |