Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
1898 conjugacy classes of subgroups.
The subgroup lattice has 248 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C131 | C25 |
| commutator | C22 | C24×C4×C131 |
| Frattini, cosocle | C23 | C25×C131 |
| prime radical | C24×C131 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2381×C131 | C2 | semidirect |
| 3. #2371×C131 | C2 | semidirect |
| 4. #2355×C131 | C2 | semidirect |
| 8. #533×C131 | C4 | semidirect |
| 123. #34375 | C131 | direct (N × H) |
| 124. C131 | #34375 | direct (N × H) |
| 126. #2381 | C2×C131 | semidirect |
| 127. #2371 | C2×C131 | semidirect |
| 128. #2355 | C2×C131 | semidirect |
| 132. #533 | C4×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#533×C131 | 2 |
| #2381×C131 | 2 |
| #2371×C131 | 2 |
| #2355×C131 | 2 |
| #2332×C131 | 2 |
| #2314×C131 | 2 |
| #2283×C131 | 2 |
| #34375 | 131 |