Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
342 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 176 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 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C31 |
| prime radical | C23×C31 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C31×#475 | C2 | semidirect |
| 4. C31×#462 | C2 | semidirect |
| 52. #3255 | C31 | direct (N × H) |
| 64. #475 | C2×C31 | semidirect |
| 66. #462 | C2×C31 | semidirect |
| 85. C31 | #3255 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#533 | 2 |
| C31×#475 | 2 |
| C31×#470 | 2 |
| C31×#462 | 2 |
| C31×#423 | 2 |
| #3255 | 31 |