Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
508 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23766580 | C2 | semidirect |
| 3. #23762125 | C2 | semidirect |
| 6. #23761265 | C2 | semidirect |
| 7. C79×#1288 | C2 | semidirect |
| 12. #19098943 | C4 | semidirect |
| 13. #19098936 | C4 | semidirect |
| 163. #1288 | D79 | semidirect |
| 164. C79 | #9429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773859 | 2 |
| #23766580 | 2 |
| #23762125 | 2 |
| #23761948 | 2 |
| #23761946 | 2 |
| #23761265 | 2 |
| C79×#1288 | 2 |
| #9429 | 79 |