Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
438 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | #386 |
| commutator | C22×C4 | C22×C4×C31 |
| Frattini, cosocle | C2×C42 | C23×C31 |
| prime radical | C31×#3213 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C31×#2980 | C2 | semidirect |
| 3. C31×#1553 | C2 | semidirect |
| 4. C31×#1533 | C2 | semidirect |
| 5. C31×#1469 | C2 | semidirect |
| 6. C31×#1308 | C2 | semidirect |
| 7. C31×#1287 | C2 | semidirect |
| 106. #9333 | C31 | direct (N × H) |
| 142. #2980 | C2×C31 | semidirect |
| 143. #1553 | C2×C31 | semidirect |
| 144. #1533 | C2×C31 | semidirect |
| 145. #1469 | C2×C31 | semidirect |
| 146. #1308 | C2×C31 | semidirect |
| 147. #1287 | C2×C31 | semidirect |
| 231. C31 | #9333 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#3213 | 2 |
| C31×#2980 | 2 |
| C31×#1553 | 2 |
| C31×#1533 | 2 |
| C31×#1469 | 2 |
| C31×#1308 | 2 |
| C31×#1287 | 2 |
| #9333 | 31 |