Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
492 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23764376 | C2 | semidirect |
| 4. C4×#14579071 | C2 | semidirect |
| 5. #23762158 | C2 | semidirect |
| 6. #23761856 | C2 | semidirect |
| 9. #19098959 | C4 | semidirect |
| 10. #19098935 | C4 | semidirect |
| 11. #19098915 | C4 | semidirect |
| 12. #19098909 | C4 | semidirect |
| 141. C79⋊C8 | #104 | semidirect |
| 173. C79 | #9851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773955 | 2 |
| #23764376 | 2 |
| #23764229 | 2 |
| C4×#14579071 | 2 |
| #23762158 | 2 |
| #23761856 | 2 |
| C79×#1492 | 2 |
| #9851 | 79 |