Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
284 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 284 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, socle | C2×C31 | #1530 |
| commutator | C42 | C22×C4×C31 |
| Frattini, cosocle | #97 | C23×C31 |
| prime radical | C31×#540 | C4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C31×#405 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C31×#2166 | C2 | semidirect |
| 3. C31×#2110 | C2 | semidirect |
| 4. C31×#1356 | C2 | semidirect |
| 5. C31×#1355 | C2 | semidirect |
| 87. #11912 | C31 | direct (N × H) |
| 112. #2166 | C2×C31 | semidirect |
| 113. #2110 | C2×C31 | semidirect |
| 114. #1356 | C2×C31 | semidirect |
| 115. #1355 | C2×C31 | semidirect |
| 182. C31 | #11912 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#3174 | 2 |
| C31×#2166 | 2 |
| C31×#2110 | 2 |
| C31×#1356 | 2 |
| C31×#1355 | 2 |
| #11912 | 31 |