Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
246 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 92 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 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C31 |
| prime radical | C23×C31 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C22×C4×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 23. M16×C31 | Q8 | semidirect |
| 35. C42×C31 | Q8 | semidirect |
| 52. #2060 | C31 | direct (N × H) |
| 86. C31 | #2060 | direct (N × H) |
| 93. M16 | Q8×C31 | semidirect |
| 105. C42 | Q8×C31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#544 | 2 |
| C31×#428 | 2 |
| C31×#384 | 2 |
| C31×#343 | 2 |
| C31×#339 | 2 |
| #2060 | 31 |