Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
306 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C131 |
| prime radical | C2×#41×C131 | D4 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C22×C4×C131 ◁ #408×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2236×C131 | C2 | semidirect |
| 3. #2235×C131 | C2 | semidirect |
| 5. #1350×C131 | C2 | semidirect |
| 6. #1350×C131 | C2 | semidirect |
| 150. #12286 | C131 | direct (N × H) |
| 151. C131 | #12286 | direct (N × H) |
| 153. #2236 | C2×C131 | semidirect |
| 154. #2235 | C2×C131 | semidirect |
| 156. #1350 | C2×C131 | semidirect |
| 157. #1350 | C2×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3202×C131 | 2 |
| #2236×C131 | 2 |
| #2235×C131 | 2 |
| #2078×C131 | 2 |
| #1350×C131 | 2 |
| #1315×C131 | 2 |
| #12286 | 131 |