Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
590 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 214 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 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C131 |
| prime radical | C24×C131 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C23×C4×C131 ◁ C23×C8×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2236×C131 | C2 | semidirect |
| 3. #2216×C131 | C2 | semidirect |
| 4. #2188×C131 | C2 | semidirect |
| 9. C2×Q32×C131 | C22 | semidirect |
| 17. #366×C131 | C22 | semidirect |
| 18. #358×C131 | C22 | semidirect |
| 75. C23×C131 | Q32 | semidirect |
| 116. #33755 | C131 | direct (N × H) |
| 117. C131 | #33755 | direct (N × H) |
| 119. #2236 | C2×C131 | semidirect |
| 120. #2216 | C2×C131 | semidirect |
| 121. #2188 | C2×C131 | semidirect |
| 126. C2×Q32 | C22×C131 | semidirect |
| 134. #366 | C22×C131 | semidirect |
| 135. #358 | C22×C131 | semidirect |
| 192. C23 | Q32×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#467×C131 | 2 |
| #2236×C131 | 2 |
| #2216×C131 | 2 |
| #2188×C131 | 2 |
| C2×C22⋊C16×C131 | 2 |
| #33755 | 131 |