Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
996 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 1. #23774787 | C2 | semidirect |
| 2. #23773722 | C2 | semidirect |
| 3. #23762628 | C2 | semidirect |
| 4. #23762579 | C2 | semidirect |
| 5. #23762135 | C2 | semidirect |
| 6. #23761851 | C2 | semidirect |
| 8. #19099120 | C22 | semidirect |
| 10. #19098913 | C22 | semidirect |
| 13. #19098843 | C22 | semidirect |
| 15. #19098768 | C22 | semidirect |
| 17. #19098587 | C22 | semidirect |
| 19. C2×C4×C79⋊C8 | C22 | semidirect |
| 20. #19098312 | C22 | semidirect |
| 22. D4⋊(C79⋊C8) | C22 | semidirect |
| 187. C79 | #18691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774787 | 2 |
| #23773722 | 2 |
| #23762628 | 2 |
| #23762579 | 2 |
| #23762135 | 2 |
| #23761851 | 2 |
| C79×#3549 | 2 |
| #18691 | 79 |