Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
542 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 542 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. #23766285 | C2 | semidirect |
| 3. #23763499 | C2 | semidirect |
| 5. #23761305 | C2 | semidirect |
| 6. #23761285 | C2 | semidirect |
| 26. #428×C79 | C4 | semidirect |
| 27. #418×C79 | C4 | semidirect |
| 210. C79 | #9367 | semidirect |
| 216. #428 | Dic79 | semidirect |
| 217. #418 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766285 | 2 |
| #23764237 | 2 |
| #23763499 | 2 |
| #23761916 | 2 |
| #23761305 | 2 |
| #23761285 | 2 |
| C79×#3094 | 2 |
| #9367 | 79 |