Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
476 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 253 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. #23757316 | C2 | semidirect |
| 4. #23757313 | C2 | semidirect |
| 5. #23757309 | C2 | semidirect |
| 6. C2×#19097702 | C2 | semidirect |
| 8. #19097778 | C4 | semidirect |
| 26. #14578938 | C2×C4 | semidirect |
| 27. C2×#11929434 | C2×C4 | semidirect |
| 76. C157 | #2912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097778 | 2 |
| #23757756 | 2 |
| #23757316 | 2 |
| #23757313 | 2 |
| #23757309 | 2 |
| C2×#19097702 | 2 |
| #520×C157 | 2 |
| #2912 | 157 |