Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
642 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23774315 | C2 | semidirect |
| 2. #23773853 | C2 | semidirect |
| 3. #23764239 | C2 | semidirect |
| 4. #23761992 | C2 | semidirect |
| 5. #23761817 | C2 | semidirect |
| 6. #23761289 | C2 | semidirect |
| 7. C79×#3253 | C2 | semidirect |
| 204. #3253 | D79 | semidirect |
| 211. C79 | #10104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774315 | 2 |
| #23773853 | 2 |
| #23764239 | 2 |
| #23761992 | 2 |
| #23761817 | 2 |
| #23761289 | 2 |
| C79×#3253 | 2 |
| #10104 | 79 |