Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
378 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23773940 | C2 | semidirect |
| 4. #23761509 | C2 | semidirect |
| 5. #23761495 | C2 | semidirect |
| 6. #23761490 | C2 | semidirect |
| 54. 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 |
|---|---|
| #23773940 | 2 |
| C2×#19098364 | 2 |
| #23764311 | 2 |
| #23761509 | 2 |
| #23761495 | 2 |
| #23761490 | 2 |
| C79×#2140 | 2 |
| #13369 | 79 |