Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1770 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 1770 conjugacy classes of subgroups — too many to draw. Only its 451 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×#19098431 | C2 | semidirect |
| 2. C2×C42×Dic79 | C2 | semidirect |
| 4. #23761632 | C2 | semidirect |
| 14. C2×#126×C79 | C4 | semidirect |
| 61. C42×C79 | C22⋊C4 | semidirect |
| 85. C2×Dic79 | #126 | semidirect |
| 111. C79 | #14711 | semidirect |
| 114. C2×#126 | Dic79 | semidirect |
| 167. C42 | C22⋊Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098431 | 2 |
| C2×C42×Dic79 | 2 |
| #23761637 | 2 |
| #23761632 | 2 |
| C22×#126×C79 | 2 |
| #14711 | 79 |