Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
396 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 110 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 | #1519 |
| commutator | C2×C8 | C22×C4×C31 |
| Frattini, cosocle | C2×M16 | C23×C31 |
| prime radical | C31×#3058 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C2×C31×#131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C31×#2115 | C2 | semidirect |
| 3. C31×#1812 | C2 | semidirect |
| 4. C31×#1339 | C2 | semidirect |
| 5. C22×D8×C31 | C4 | semidirect |
| 9. C31×#469 | C4 | semidirect |
| 14. C31×#427 | C4 | semidirect |
| 18. C31×#349 | C22 | semidirect |
| 19. C31×H(3,ℤ/4) | C22 | semidirect |
| 94. #11868 | C31 | direct (N × H) |
| 128. #2115 | C2×C31 | semidirect |
| 129. #1812 | C2×C31 | semidirect |
| 130. #1339 | C2×C31 | semidirect |
| 149. C22×D8 | C4×C31 | semidirect |
| 153. #469 | C4×C31 | semidirect |
| 158. #427 | C4×C31 | semidirect |
| 162. #349 | C22×C31 | semidirect |
| 163. H(3,ℤ/4) | C22×C31 | semidirect |
| 203. C31 | #11868 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#3058 | 2 |
| C31×#2115 | 2 |
| C31×#1812 | 2 |
| C31×#1339 | 2 |
| #11868 | 31 |