Order 9472.
810 conjugacy classes of subgroups.
The subgroup lattice has 336 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C37 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C37 |
| Frattini, cosocle | C23×C4 | C23×C37 |
| socle | C22×C37 | C2×#95 |
| prime radical | C24×C37 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C37 ◁ C22×C42×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. C37×#423 | C4 | semidirect |
| 14. C37×#423 | C4 | semidirect |
| 16. C2×C4⋊C8×C37 | C4 | semidirect |
| 140. #10856 | C37 | direct (N × H) |
| 155. C4×C37 | #344 | semidirect |
| 180. #423 | C4×C37 | semidirect |
| 181. #423 | C4×C37 | semidirect |
| 183. C2×C4⋊C8 | C4×C37 | semidirect |
| 189. C37 | #10856 | direct (N × H) |
| 322. C4 | C37×#344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C37×#423 | 2 |
| C4×#117×C37 | 2 |
| C2×C37×#344 | 2 |
| #10856 | 37 |