Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
500 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 94 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 | #394 |
| commutator, Frattini, cosocle | C23×C4 | C23×C131 |
| prime radical | #3186×C131 | C2 |
| LCS | G ▷ C23×C4 ▷ 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. #1900×C131 | C2 | semidirect |
| 3. #1851×C131 | C2 | semidirect |
| 4. #1507×C131 | C2 | semidirect |
| 5. #1293×C131 | C2 | semidirect |
| 156. #10557 | C131 | direct (N × H) |
| 157. C131 | #10557 | direct (N × H) |
| 159. #1900 | C2×C131 | semidirect |
| 160. #1851 | C2×C131 | semidirect |
| 161. #1507 | C2×C131 | semidirect |
| 162. #1293 | C2×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3186×C131 | 2 |
| #1900×C131 | 2 |
| #1851×C131 | 2 |
| #1507×C131 | 2 |
| #1293×C131 | 2 |
| #10557 | 131 |