Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
542 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23766585 | C2 | semidirect |
| 5. C2×#19098304 | C2 | semidirect |
| 6. #23761282 | C2 | semidirect |
| 7. C79×#1295 | C2 | semidirect |
| 11. #19098928 | C4 | semidirect |
| 224. #1295 | D79 | semidirect |
| 225. C79 | #9002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098928 | 2 |
| #23766585 | 2 |
| #23764224 | 2 |
| #23764223 | 2 |
| C2×#19098304 | 2 |
| #23761282 | 2 |
| C79×#1295 | 2 |
| #9002 | 79 |