Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23766003 | C2 | semidirect |
| 3. #23761730 | C2 | semidirect |
| 4. #23761286 | C2 | semidirect |
| 15. #400×C79 | C4 | semidirect |
| 16. #394×C79 | C4 | semidirect |
| 158. C79 | #9414 | semidirect |
| 162. #400 | Dic79 | semidirect |
| 163. #394 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766003 | 2 |
| #23761916 | 2 |
| #23761730 | 2 |
| #23761286 | 2 |
| C79×#2591 | 2 |
| #9414 | 79 |