Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #23778775 | C2 | semidirect |
| 2. #23778773 | C2 | semidirect |
| 3. #23778770 | C2 | semidirect |
| 4. #23778766 | C2 | semidirect |
| 5. #23778764 | C2 | semidirect |
| 6. #23778761 | C2 | semidirect |
| 7. #23778757 | C2 | semidirect |
| 9. C4×Dic634 | C2 | semidirect |
| 10. C4×C22⋊D317 | C2 | semidirect |
| 11. C4×C22⋊D317 | C2 | semidirect |
| 12. #23778739 | C2 | semidirect |
| 13. #23778737 | C2 | semidirect |
| 14. C2×C4×Dic317 | C2 | semidirect |
| 15. C4×D4×C317 | C2 | semidirect |
| 103. C317 | #529 | semidirect |
| 116. C4×D4 | D317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23778775 | 2 |
| #23778773 | 2 |
| #23778770 | 2 |
| #23778766 | 2 |
| #23778764 | 2 |
| #23778761 | 2 |
| #23778757 | 2 |
| #23778752 | 2 |
| C4×Dic634 | 2 |
| C4×C22⋊D317 | 2 |
| #23778739 | 2 |
| #23778737 | 2 |
| C2×C4×Dic317 | 2 |
| C4×D4×C317 | 2 |
| #529 | 317 |