Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
698 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#19098287 | C2 | semidirect |
| 3. #23761420 | C2 | semidirect |
| 4. #23761396 | C2 | semidirect |
| 5. C79×#1819 | C2 | semidirect |
| 6. C22×#11929624 | C4 | semidirect |
| 9. #19098475 | C4 | semidirect |
| 11. #19098472 | C4 | semidirect |
| 16. #19098426 | C4 | semidirect |
| 236. #1819 | D79 | semidirect |
| 240. C79 | #11839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766719 | 2 |
| C2×#19098287 | 2 |
| #23761420 | 2 |
| #23761396 | 2 |
| C79×#1819 | 2 |
| #11839 | 79 |