Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
360 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. #23763281 | C2 | semidirect |
| 5. #23761508 | C2 | semidirect |
| 6. #23761481 | C2 | semidirect |
| 7. C79×#2159 | C2 | semidirect |
| 15. #19098377 | C4 | semidirect |
| 150. #2159 | D79 | semidirect |
| 157. C79 | #13136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098377 | 2 |
| #23765115 | 2 |
| #23764264 | 2 |
| #23763281 | 2 |
| #23761508 | 2 |
| #23761481 | 2 |
| C79×#2159 | 2 |
| #13136 | 79 |