Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
802 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 222 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 | #381 |
| commutator | C24 | C22×C4×C31 |
| Frattini, cosocle | C23×C4 | C23×C31 |
| prime radical | C24×C31 | C22×C4 |
| LCS | G ▷ C24 ▷ 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 |
|---|---|---|
| 60. #11168 | C31 | direct (N × H) |
| 126. C31 | #11168 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C31×#101 | 2 |
| C31×#2310 | 2 |
| C2×C31×#344 | 2 |
| #11168 | 31 |