Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
232 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 1. #23758284 | C2 | semidirect |
| 4. #23758239 | C2 | semidirect |
| 5. #23758152 | C2 | semidirect |
| 6. #23758148 | C2 | semidirect |
| 23. #19097688 | C4 | semidirect |
| 24. #19097687 | C4 | semidirect |
| 25. #19097687 | C4 | semidirect |
| 26. #100×C157 | C4 | semidirect |
| 114. C157 | #1931 | semidirect |
| 139. #100 | #10597845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758284 | 2 |
| #23758265 | 2 |
| C2×#19097833 | 2 |
| #23758239 | 2 |
| #23758152 | 2 |
| #23758148 | 2 |
| #100×D157 | 2 |
| #1931 | 157 |