Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
300 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 104 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 | C2×C22⋊C4 |
| commutator | C23 | C22×C4×C31 |
| Frattini, cosocle | C24 | C23×C31 |
| prime radical | C24×C31 | C23 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C2×C4⋊C4×C31 | C4 | semidirect |
| 9. C2×C42×C31 | C4 | semidirect |
| 35. #1820 | C31 | direct (N × H) |
| 55. C2×C4⋊C4 | C4×C31 | semidirect |
| 58. C2×C42 | C4×C31 | semidirect |
| 60. C31 | #1820 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C31×#117 | 2 |
| C31×#381 | 2 |
| C31×#342 | 2 |
| #1820 | 31 |