Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1068 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1068 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. C2×#19099299 | C2 | semidirect |
| 2. #23773518 | C2 | semidirect |
| 3. #23762519 | C2 | semidirect |
| 4. #23762457 | C2 | semidirect |
| 5. #23762114 | C2 | semidirect |
| 6. #23761848 | C2 | semidirect |
| 16. #19098855 | C22 | semidirect |
| 17. #19098760 | C22 | semidirect |
| 22. #19098295 | C22 | semidirect |
| 172. C79 | #18526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099299 | 2 |
| #23773518 | 2 |
| #23762519 | 2 |
| #23762457 | 2 |
| #23762114 | 2 |
| #23761848 | 2 |
| C79×#3151 | 2 |
| #18526 | 79 |