Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
2486 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 2486 conjugacy classes of subgroups — too many to draw. Only its 174 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×C131 | #379 |
| commutator | C24 | C22×C4×C131 |
| Frattini, cosocle | C23×C4 | C23×C131 |
| prime radical | C22×#120×C131 | C2 |
| LCS | G ▷ C24 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1783×C131 | C2 | semidirect |
| 3. #1462×C131 | C2 | semidirect |
| 12. #407×C131 | C22 | semidirect |
| 117. C23×C131 | #100 | semidirect |
| 163. #8547 | C131 | direct (N × H) |
| 164. C131 | #8547 | direct (N × H) |
| 166. #1783 | C2×C131 | semidirect |
| 167. #1462 | C2×C131 | semidirect |
| 176. #407 | C22×C131 | semidirect |
| 281. C23 | #100×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#120×C131 | 2 |
| #1783×C131 | 2 |
| #1462×C131 | 2 |
| #8547 | 131 |