Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
460 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #23764344 | C2 | semidirect |
| 3. C4×#14579094 | C2 | semidirect |
| 4. #23761898 | C2 | semidirect |
| 6. #23761687 | C2 | semidirect |
| 9. #19098959 | C4 | semidirect |
| 10. #19098935 | C4 | semidirect |
| 11. #19098915 | C4 | semidirect |
| 12. #19098909 | C4 | semidirect |
| 163. C79⋊C8 | #104 | semidirect |
| 198. C79 | #9722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773955 | 2 |
| #23764344 | 2 |
| C4×#14579094 | 2 |
| #23761898 | 2 |
| #23761895 | 2 |
| #23761687 | 2 |
| C79×#1980 | 2 |
| #9722 | 79 |