Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1004 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 163 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. #23777814 | C2 | semidirect |
| 2. #23774341 | C2 | semidirect |
| 3. #23762476 | C2 | semidirect |
| 4. #23762457 | C2 | semidirect |
| 5. #23762062 | C2 | semidirect |
| 6. #23761822 | C2 | semidirect |
| 9. #19099299 | C22 | semidirect |
| 10. #19099293 | C22 | semidirect |
| 21. #19098312 | C22 | semidirect |
| 22. #19098307 | C22 | semidirect |
| 23. #19098295 | C22 | semidirect |
| 175. C79 | #18718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777814 | 2 |
| #23774341 | 2 |
| #23762476 | 2 |
| #23762457 | 2 |
| #23762062 | 2 |
| #23761822 | 2 |
| C79×#3151 | 2 |
| #18718 | 79 |