Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
378 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23773939 | C2 | semidirect |
| 4. #23761510 | C2 | semidirect |
| 5. #23761497 | C2 | semidirect |
| 6. #23761489 | C2 | semidirect |
| 51. C2×D8×C79 | Q8 | semidirect |
| 166. C79 | #13369 | semidirect |
| 190. C2×D8 | Dic158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773939 | 2 |
| #23765116 | 2 |
| C2×#19098364 | 2 |
| #23761510 | 2 |
| #23761497 | 2 |
| #23761489 | 2 |
| C79×#1978 | 2 |
| #13369 | 79 |