Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
248 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D31 |
| commutator, socle, prime radical | C23×C31 | C22×C4 |
| Fitting | C31×#336 | C2 |
| cosocle | C22×C4×C31 | C23 |
| hypercenter | #336 | D31 |
| hypocenter | C31 | #1940 |
| LCS | G ▷ C23×C31 ▷ C31 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 126. C31 | #1940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C31⋊C8) | 2 |
| C2×Dic31⋊C8 | 2 |
| C2×#11758403 | 2 |
| C4×Dic31⋊C4 | 2 |
| #14520803 | 2 |
| C31×#336 | 2 |
| #1940 | 31 |