Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
484 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 91 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. #23771672 | C2 | semidirect |
| 3. #23761282 | C2 | semidirect |
| 4. #23761281 | C2 | semidirect |
| 39. #127×C79 | Q8 | semidirect |
| 148. C79 | #10358 | semidirect |
| 169. #127 | Dic158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771672 | 2 |
| #23764225 | 2 |
| #23761282 | 2 |
| #23761281 | 2 |
| C79×#1961 | 2 |
| #10358 | 79 |