Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
632 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 632 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 |
|---|---|---|
| 2. #23772464 | C2 | semidirect |
| 3. #23765083 | C2 | semidirect |
| 4. #23763351 | C2 | semidirect |
| 5. #23761523 | C2 | semidirect |
| 6. #23761522 | C2 | semidirect |
| 7. C79×#1791 | C2 | semidirect |
| 265. #1791 | D79 | semidirect |
| 268. C79 | #13051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772749 | 2 |
| #23772464 | 2 |
| #23765083 | 2 |
| #23763351 | 2 |
| #23761523 | 2 |
| #23761522 | 2 |
| C79×#1791 | 2 |
| #13051 | 79 |