Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
564 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23774707 | C2 | semidirect |
| 2. #23773491 | C2 | semidirect |
| 3. #23764199 | C2 | semidirect |
| 4. #23762012 | C2 | semidirect |
| 5. #23762011 | C2 | semidirect |
| 6. #23761269 | C2 | semidirect |
| 7. C79×#3109 | C2 | semidirect |
| 217. #3109 | D79 | semidirect |
| 222. C79 | #10026 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774707 | 2 |
| #23773491 | 2 |
| #23764199 | 2 |
| #23762012 | 2 |
| #23762011 | 2 |
| #23761269 | 2 |
| C79×#3109 | 2 |
| #10026 | 79 |