Order 1792.
2166 conjugacy classes of subgroups.
The subgroup lattice has 402 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D7 |
| commutator | C23×C7 | C23×C4 |
| Fitting | C2×C7×#380 | C2 |
| socle, cosocle | C24×C7 | C24 |
| prime radical | C25×C7 | C23 |
| hypercenter | C2×#380 | D7 |
| hypocenter | C7 | #13923 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C2×#380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11729320 | C2 | semidirect |
| 7. #11727159 | C2 | semidirect |
| 16. C22×Dic7⋊C4 | C4 | semidirect |
| 366. C7 | #13923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic7⋊C4 | 2 |
| C2×C7×#380 | 2 |
| C2×C4×C22⋊Dic7 | 2 |
| #11729320 | 2 |
| #11729298 | 2 |
| #11727159 | 2 |
| #13923 | 7 |