Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
712 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23771850 | C2 | semidirect |
| 3. #23763345 | C2 | semidirect |
| 4. #23761760 | C2 | semidirect |
| 5. #23761276 | C2 | semidirect |
| 6. #23761248 | C2 | semidirect |
| 7. C79×#1507 | C2 | semidirect |
| 9. C22×#11929612 | C4 | semidirect |
| 10. C22×#11929609 | C4 | semidirect |
| 18. C2×#14579084 | C4 | semidirect |
| 19. C2×#14579081 | C4 | semidirect |
| 285. #1507 | D79 | semidirect |
| 289. C79 | #9241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098706 | 2 |
| #23771850 | 2 |
| #23763345 | 2 |
| #23761760 | 2 |
| #23761276 | 2 |
| #23761248 | 2 |
| C79×#1507 | 2 |
| #9241 | 79 |