Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
688 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 202 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 |
| 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 |
|---|---|---|
| 1. C2×#466×C131 | C2 | semidirect |
| 2. #2233×C131 | C2 | semidirect |
| 3. #2218×C131 | C2 | semidirect |
| 4. #2184×C131 | C2 | semidirect |
| 5. #2112×C131 | C2 | semidirect |
| 6. C22×D8×C131 | C22 | semidirect |
| 9. C2×D16×C131 | C22 | semidirect |
| 10. C2×M32×C131 | C22 | semidirect |
| 14. #466×C131 | C22 | semidirect |
| 15. C2×#107×C131 | C22 | semidirect |
| 17. #367×C131 | C22 | semidirect |
| 18. #357×C131 | C22 | semidirect |
| 19. C22⋊C16×C131 | C22 | semidirect |
| 122. #33758 | C131 | direct (N × H) |
| 123. C131 | #33758 | direct (N × H) |
| 124. C2×#466 | C2×C131 | semidirect |
| 125. #2233 | C2×C131 | semidirect |
| 126. #2218 | C2×C131 | semidirect |
| 127. #2184 | C2×C131 | semidirect |
| 128. #2112 | C2×C131 | semidirect |
| 129. C22×D8 | C22×C131 | semidirect |
| 132. C2×D16 | C22×C131 | semidirect |
| 133. C2×M32 | C22×C131 | semidirect |
| 137. #466 | C22×C131 | semidirect |
| 138. C2×#107 | C22×C131 | semidirect |
| 140. #367 | C22×C131 | semidirect |
| 141. #357 | C22×C131 | semidirect |
| 142. C22⋊C16 | C22×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#466×C131 | 2 |
| #2233×C131 | 2 |
| #2218×C131 | 2 |
| #2184×C131 | 2 |
| #2112×C131 | 2 |
| #33758 | 131 |