Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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. #23778779 | C2 | semidirect |
| 2. #23778778 | C2 | semidirect |
| 3. #23778775 | C2 | semidirect |
| 4. #23778775 | C2 | semidirect |
| 5. #23778773 | C2 | semidirect |
| 6. #23778773 | C2 | semidirect |
| 7. #23778771 | C2 | semidirect |
| 8. #23778770 | C2 | semidirect |
| 12. #23778759 | C2 | semidirect |
| 13. #23778758 | C2 | semidirect |
| 14. #23778756 | C2 | semidirect |
| 15. C22⋊Q8×C317 | C2 | semidirect |
| 97. C317 | #563 | semidirect |
| 113. C22⋊Q8 | D317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23778779 | 2 |
| #23778778 | 2 |
| #23778775 | 2 |
| #23778773 | 2 |
| #23778771 | 2 |
| #23778770 | 2 |
| #23778766 | 2 |
| #23778763 | 2 |
| #23778762 | 2 |
| #23778759 | 2 |
| #23778758 | 2 |
| #23778756 | 2 |
| C22⋊Q8×C317 | 2 |
| #563 | 317 |