Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
498 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C31 |
| prime radical | C31×#3100 | C2 |
| LCS | G ▷ C2×C42 ▷ 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 |
|---|---|---|
| 1. C31×#3235 | C2 | semidirect |
| 2. C31×#3110 | C2 | semidirect |
| 4. C31×#1536 | C2 | semidirect |
| 5. C31×#1497 | C2 | semidirect |
| 6. C31×#1466 | C2 | semidirect |
| 7. C31×#1287 | C2 | semidirect |
| 128. #10042 | C31 | direct (N × H) |
| 168. #3235 | C2×C31 | semidirect |
| 169. #3110 | C2×C31 | semidirect |
| 171. #1536 | C2×C31 | semidirect |
| 172. #1497 | C2×C31 | semidirect |
| 173. #1466 | C2×C31 | semidirect |
| 174. #1287 | C2×C31 | semidirect |
| 277. C31 | #10042 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#3235 | 2 |
| C31×#3110 | 2 |
| C31×#3100 | 2 |
| C31×#1536 | 2 |
| C31×#1497 | 2 |
| C31×#1466 | 2 |
| C31×#1287 | 2 |
| #10042 | 31 |