Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
334 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C131 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C131 |
| socle | C22×C131 | #399 |
| prime radical | #532×C131 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C131 ◁ C2×C42×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #1832×C131 | C2 | semidirect |
| 3. #1571×C131 | C2 | semidirect |
| 4. #1570×C131 | C2 | semidirect |
| 7. #1274×C131 | C2 | semidirect |
| 128. #10665 | C131 | direct (N × H) |
| 129. C131 | #10665 | direct (N × H) |
| 131. #1832 | C2×C131 | semidirect |
| 132. #1571 | C2×C131 | semidirect |
| 133. #1570 | C2×C131 | semidirect |
| 136. #1274 | C2×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #1963×C131 | 2 |
| #1832×C131 | 2 |
| #1571×C131 | 2 |
| #1570×C131 | 2 |
| #1480×C131 | 2 |
| #1274×C131 | 2 |
| #10665 | 131 |