Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
310 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C131 | #99 |
| commutator | C2×C4 | C4×C8×C131 |
| Frattini, cosocle | C22×M16 | C22×C131 |
| socle | C22×C131 | #323 |
| prime radical | C24×C131 | M16 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C131 ◁ C22×C4×C131 ◁ C22×M16×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. #349×C131 | C4 | semidirect |
| 111. #7194 | C131 | direct (N × H) |
| 112. C131 | #7194 | direct (N × H) |
| 120. #349 | C4×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#349×C131 | 2 |
| #1729×C131 | 2 |
| #7194 | 131 |