Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
516 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 516 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 |
|---|---|---|
| 2. #23764377 | C2 | semidirect |
| 3. C42×C79⋊C8 | C2 | semidirect |
| 4. #23762155 | C2 | semidirect |
| 5. #23761854 | C2 | semidirect |
| 9. #19098959 | C4 | semidirect |
| 10. #19098935 | C4 | semidirect |
| 11. #19098915 | C4 | semidirect |
| 12. #19098909 | C4 | semidirect |
| 105. C42×C79 | SD16 | semidirect |
| 141. C79⋊C8 | #104 | semidirect |
| 173. C79 | #9843 | semidirect |
| 271. C42 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773955 | 2 |
| #23764377 | 2 |
| C42×C79⋊C8 | 2 |
| #23762155 | 2 |
| #23761854 | 2 |
| #23761851 | 2 |
| C79×#1962 | 2 |
| #9843 | 79 |