Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
348 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C31 |
| prime radical | C31×#3191 | C2 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C2×C31×C22⋊C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C31×#2235 | C2 | semidirect |
| 3. C31×#2232 | C2 | semidirect |
| 4. C31×#2075 | C2 | semidirect |
| 5. C31×#1348 | C2 | semidirect |
| 6. C31×#1347 | C2 | semidirect |
| 7. C31×#1314 | C2 | semidirect |
| 102. #12280 | C31 | direct (N × H) |
| 141. #2235 | C2×C31 | semidirect |
| 142. #2232 | C2×C31 | semidirect |
| 143. #2075 | C2×C31 | semidirect |
| 144. #1348 | C2×C31 | semidirect |
| 145. #1347 | C2×C31 | semidirect |
| 146. #1314 | C2×C31 | semidirect |
| 228. C31 | #12280 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#3191 | 2 |
| C31×#2235 | 2 |
| C31×#2232 | 2 |
| C31×#2075 | 2 |
| C31×#1348 | 2 |
| C31×#1347 | 2 |
| C31×#1314 | 2 |
| #12280 | 31 |