Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
492 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 2. #23764345 | C2 | semidirect |
| 3. #23761912 | C2 | semidirect |
| 5. #23761292 | C2 | semidirect |
| 6. #23761257 | C2 | semidirect |
| 24. #474×C79 | C4 | semidirect |
| 25. #461×C79 | C4 | semidirect |
| 189. C79 | #9327 | semidirect |
| 193. #474 | Dic79 | semidirect |
| 194. #461 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766043 | 2 |
| #23764345 | 2 |
| #23761912 | 2 |
| #23761843 | 2 |
| #23761292 | 2 |
| #23761257 | 2 |
| C79×#3110 | 2 |
| #9327 | 79 |