Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
292 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C131 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23×C131 |
| socle | C2×C131 | #2076 |
| prime radical | C24×C131 | Q16 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C131 ◁ C22×C4×C131 ◁ C23×C8×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2161×C131 | C2 | semidirect |
| 4. #1388×C131 | C2 | semidirect |
| 5. #1385×C131 | C2 | semidirect |
| 92. #13498 | C131 | direct (N × H) |
| 93. C131 | #13498 | direct (N × H) |
| 94. #2161 | C2×C131 | semidirect |
| 97. #1388 | C2×C131 | semidirect |
| 98. #1385 | C2×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2161×C131 | 2 |
| #2112×C131 | 2 |
| #1810×C131 | 2 |
| #1388×C131 | 2 |
| #1385×C131 | 2 |
| #13498 | 131 |