Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
416 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23765065 | C2 | semidirect |
| 2. #23761565 | C2 | semidirect |
| 3. #23761563 | C2 | semidirect |
| 9. #532×C79 | C4 | semidirect |
| 12. #494×C79 | C4 | semidirect |
| 14. #492×C79 | C4 | semidirect |
| 16. C2×C4×C8×C79 | C4 | semidirect |
| 129. C79 | #13583 | semidirect |
| 131. #532 | Dic79 | semidirect |
| 134. #494 | Dic79 | semidirect |
| 136. #492 | Dic79 | semidirect |
| 139. C2×C4×C8 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765065 | 2 |
| #23761565 | 2 |
| #23761563 | 2 |
| C79×#3147 | 2 |
| #13583 | 79 |