Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
204 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 55 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. C2×#19098403 | C2 | semidirect |
| 4. #23765258 | C2 | semidirect |
| 5. Dic79⋊C32 | C2 | semidirect |
| 7. C79×#1416 | C2 | semidirect |
| 99. #1416 | D79 | semidirect |
| 101. C79 | #13690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098403 | 2 |
| C2×#19098402 | 2 |
| #23765662 | 2 |
| #23765258 | 2 |
| Dic79⋊C32 | 2 |
| #23761577 | 2 |
| C79×#1416 | 2 |
| #13690 | 79 |