Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23763531 | C2 | semidirect |
| 4. #23761259 | C2 | semidirect |
| 5. C79×#1564 | C2 | semidirect |
| 9. #19098642 | C4 | semidirect |
| 11. C8×D316 | C4 | semidirect |
| 137. #1564 | D79 | semidirect |
| 140. C79 | #8678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772113 | 2 |
| #23763531 | 2 |
| #23761961 | 2 |
| #23761259 | 2 |
| C79×#1564 | 2 |
| #8678 | 79 |