Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
1598 conjugacy classes of subgroups.
The subgroup lattice has 350 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C31 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C31 |
| prime radical | C24×C31 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C31×#2612 | C2 | semidirect |
| 5. C31×#2606 | C2 | semidirect |
| 6. C31×#2605 | C2 | semidirect |
| 59. C2×C42×C31 | Q8 | semidirect |
| 117. #35120 | C31 | direct (N × H) |
| 154. #2612 | C2×C31 | semidirect |
| 155. #2606 | C2×C31 | semidirect |
| 156. #2605 | C2×C31 | semidirect |
| 233. C2×C42 | Q8×C31 | semidirect |
| 251. C31 | #35120 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#2855 | 2 |
| C31×#2659 | 2 |
| C31×#2646 | 2 |
| C31×#2612 | 2 |
| C31×#2606 | 2 |
| C31×#2605 | 2 |
| C31×#2329 | 2 |
| C31×#2283 | 2 |
| C2×C31×#376 | 2 |
| #35120 | 31 |