Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23757617 | C2 | semidirect |
| 4. #23757616 | C2 | semidirect |
| 5. #23757610 | C2 | semidirect |
| 6. #23757605 | C2 | semidirect |
| 7. #23757316 | C2 | semidirect |
| 8. #23757281 | C2 | semidirect |
| 9. C2×#19097696 | C2 | semidirect |
| 11. #427×C157 | C2 | semidirect |
| 126. C157 | #3097 | semidirect |
| 135. #427 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757849 | 2 |
| #23757753 | 2 |
| #23757617 | 2 |
| #23757616 | 2 |
| #23757610 | 2 |
| #23757605 | 2 |
| #23757316 | 2 |
| #23757281 | 2 |
| C2×#19097696 | 2 |
| #23757239 | 2 |
| #427×C157 | 2 |
| #3097 | 157 |