Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
322 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 322 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 | C23 | C4×C8×C131 |
| Frattini, cosocle | C2×#117 | C22×C131 |
| socle | C22×C131 | #342 |
| prime radical | C24×C131 | C42 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C131 ◁ C22×C4×C131 ◁ C2×#117×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. C2×M16×C131 | C8 | semidirect |
| 20. C22×C8×C131 | C8 | semidirect |
| 118. #7188 | C131 | direct (N × H) |
| 119. C131 | #7188 | direct (N × H) |
| 133. C2×M16 | C8×C131 | semidirect |
| 139. C22×C8 | C8×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #1729×C131 | 2 |
| #1458×C131 | 2 |
| #7188 | 131 |