Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
412 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 70 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 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×C4⋊C4 | C23×C31 |
| prime radical | C31×#2828 | C2 |
| LCS | G ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C23×C31 ◁ C2×C4⋊C4×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C31×#2027 | C2 | semidirect |
| 3. C31×#1617 | C2 | semidirect |
| 4. C31×#1599 | C2 | semidirect |
| 5. C31×#1353 | C2 | semidirect |
| 6. C31×#1345 | C2 | semidirect |
| 7. C31×#1318 | C2 | semidirect |
| 112. #12274 | C31 | direct (N × H) |
| 162. #2027 | C2×C31 | semidirect |
| 163. #1617 | C2×C31 | semidirect |
| 164. #1599 | C2×C31 | semidirect |
| 165. #1353 | C2×C31 | semidirect |
| 166. #1345 | C2×C31 | semidirect |
| 167. #1318 | C2×C31 | semidirect |
| 258. C31 | #12274 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#2828 | 2 |
| C31×#2027 | 2 |
| C31×#1617 | 2 |
| C31×#1599 | 2 |
| C31×#1353 | 2 |
| C31×#1345 | 2 |
| C31×#1318 | 2 |
| #12274 | 31 |