Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23761575 | C2 | semidirect |
| 5. #23761561 | C2 | semidirect |
| 6. #23761559 | C2 | semidirect |
| 7. C79×#1414 | C2 | semidirect |
| 8. #19099176 | C4 | semidirect |
| 11. #19098943 | C4 | semidirect |
| 12. #19098933 | C4 | semidirect |
| 17. #19098622 | C4 | semidirect |
| 158. #1414 | D79 | semidirect |
| 161. C79 | #13608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774486 | 2 |
| #23765086 | 2 |
| #23765073 | 2 |
| #23761575 | 2 |
| #23761561 | 2 |
| #23761559 | 2 |
| C79×#1414 | 2 |
| #13608 | 79 |