Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
348 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 90 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 | C2×C42 | C23×C131 |
| prime radical | #532×C131 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1838×C131 | C2 | semidirect |
| 3. #1559×C131 | C2 | semidirect |
| 5. #1531×C131 | C2 | semidirect |
| 7. #1307×C131 | C2 | semidirect |
| 153. #10527 | C131 | direct (N × H) |
| 154. C131 | #10527 | direct (N × H) |
| 156. #1838 | C2×C131 | semidirect |
| 157. #1559 | C2×C131 | semidirect |
| 159. #1531 | C2×C131 | semidirect |
| 161. #1307 | C2×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3254×C131 | 2 |
| #1838×C131 | 2 |
| #1559×C131 | 2 |
| #1557×C131 | 2 |
| #1531×C131 | 2 |
| #1530×C131 | 2 |
| #1307×C131 | 2 |
| #10527 | 131 |