Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
248 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8×C31 | #99 |
| commutator | C2×C4 | C4×C8×C31 |
| Frattini, cosocle | C2×#131 | C22×C31 |
| socle | C2×C31 | #1282 |
| prime radical | C2×#41×C31 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C31 ◁ C2×C8×C31 ◁ C2×C31×#131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C2×C31×M32 | C4 | semidirect |
| 7. C22×C16×C31 | C4 | semidirect |
| 12. C31×#349 | C4 | semidirect |
| 71. #7208 | C31 | direct (N × H) |
| 114. C2×M32 | C4×C31 | semidirect |
| 115. C22×C16 | C4×C31 | semidirect |
| 120. #349 | C4×C31 | semidirect |
| 153. C31 | #7208 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#2115 | 2 |
| C31×#2113 | 2 |
| C31×#1757 | 2 |
| #7208 | 31 |