Order 1792.
564 conjugacy classes of subgroups.
The subgroup lattice has 362 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C2×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| socle | C22×C7 | C2×#95 |
| prime radical | C24×C7 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C22×C42×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C7×#1300 | C2 | semidirect |
| 8. C7×#432 | C4 | semidirect |
| 9. C7×#432 | C4 | semidirect |
| 10. C7×#432 | C4 | semidirect |
| 15. C2×C7×C4⋊C8 | C4 | semidirect |
| 27. #8069 | C7 | direct (N × H) |
| 67. #1300 | C2×C7 | semidirect |
| 117. #432 | C4×C7 | semidirect |
| 118. #432 | C4×C7 | semidirect |
| 119. #432 | C4×C7 | semidirect |
| 124. C2×C4⋊C8 | C4×C7 | semidirect |
| 330. C7 | #8069 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2920 | 2 |
| C2×C7×#432 | 2 |
| C7×#2283 | 2 |
| C7×#1300 | 2 |
| #8069 | 7 |