Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
648 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 135 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. #23763468 | C2 | semidirect |
| 4. #23761278 | C2 | semidirect |
| 16. #390×C79 | C4 | semidirect |
| 17. #389×C79 | C4 | semidirect |
| 172. C79 | #9157 | semidirect |
| 177. #390 | Dic79 | semidirect |
| 178. #389 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098431 | 2 |
| #23763468 | 2 |
| C2×#19098297 | 2 |
| #23761278 | 2 |
| C79×#2854 | 2 |
| #9157 | 79 |