Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
336 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23765200 | C2 | semidirect |
| 3. #23763526 | C2 | semidirect |
| 4. #23761413 | C2 | semidirect |
| 5. #23761411 | C2 | semidirect |
| 9. #19098964 | C4 | semidirect |
| 10. #19098946 | C4 | semidirect |
| 14. #19098657 | C4 | semidirect |
| 16. D8×Dic79 | C4 | semidirect |
| 169. C79 | #11860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773965 | 2 |
| #23765200 | 2 |
| #23763526 | 2 |
| #23761413 | 2 |
| #23761411 | 2 |
| #23761409 | 2 |
| C79×#1347 | 2 |
| #11860 | 79 |