Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
428 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 182 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42×C31 | C2×D4 |
| commutator | C2×C4 | C2×C42×C31 |
| Frattini, cosocle | C2×C42 | C23×C31 |
| socle | C22×C31 | C4×C22⋊C4 |
| prime radical | C2×#41×C31 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C31 ◁ C2×C4×C8×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C31×#1452 | C2 | semidirect |
| 4. C2×C82×C31 | C2 | semidirect |
| 5. C31×#1278 | C2 | semidirect |
| 65. #8187 | C31 | direct (N × H) |
| 87. #1452 | C2×C31 | semidirect |
| 88. C2×C82 | C2×C31 | semidirect |
| 89. #1278 | C2×C31 | semidirect |
| 140. C31 | #8187 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#2922 | 2 |
| C31×#1476 | 2 |
| C31×#1452 | 2 |
| C2×C82×C31 | 2 |
| C31×#1278 | 2 |
| #8187 | 31 |