Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
498 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23772539 | C2 | semidirect |
| 3. #23764327 | C2 | semidirect |
| 4. #23762113 | C2 | semidirect |
| 5. #23761269 | C2 | semidirect |
| 6. #23761256 | C2 | semidirect |
| 7. C79×#1509 | C2 | semidirect |
| 9. #19098953 | C4 | semidirect |
| 10. #19098929 | C4 | semidirect |
| 220. #1509 | D79 | semidirect |
| 223. C79 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774415 | 2 |
| #23772539 | 2 |
| #23764327 | 2 |
| #23762113 | 2 |
| #23761269 | 2 |
| #23761256 | 2 |
| C79×#1509 | 2 |
| #9378 | 79 |