Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
196 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #23758160 | C2 | semidirect |
| 4. C16×#10597845 | C2 | semidirect |
| 8. #19097846 | C4 | semidirect |
| 9. #19097845 | C4 | semidirect |
| 16. #19097711 | C4 | semidirect |
| 17. #19097710 | C4 | semidirect |
| 19. M32×C157 | C4 | semidirect |
| 28. #14578957 | C2×C4 | semidirect |
| 35. #14578929 | C2×C4 | semidirect |
| 37. C16×C157 | C2×C4 | semidirect |
| 59. #10597845 | M32 | direct (N × H) |
| 68. C157 | C4×M32 | semidirect |
| 82. M32 | #10597845 | direct (N × H) |
| 106. C16 | C2×#10597845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D157⋊M32 | 2 |
| C2×C8×#10597845 | 2 |
| #23758160 | 2 |
| C16×#10597845 | 2 |
| M32×D157 | 2 |
| C4×M32 | 157 |