Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1258 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 207 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 |
|---|---|---|
| 1. #23774322 | C2 | semidirect |
| 2. #23768573 | C2 | semidirect |
| 3. #23762352 | C2 | semidirect |
| 4. #23761895 | C2 | semidirect |
| 5. #23761721 | C2 | semidirect |
| 7. C2×#14579161 | C22 | semidirect |
| 11. #19098701 | C22 | semidirect |
| 12. #19098616 | C22 | semidirect |
| 13. #19098475 | C22 | semidirect |
| 17. C4×C4⋊Dic79 | C22 | semidirect |
| 18. #19098297 | C22 | semidirect |
| 19. #19098287 | C22 | semidirect |
| 103. C2×D4×C79 | SD16 | semidirect |
| 201. C79 | #18388 | semidirect |
| 288. C2×D4 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774322 | 2 |
| #23768573 | 2 |
| #23762352 | 2 |
| #23761895 | 2 |
| #23761721 | 2 |
| C79×#3496 | 2 |
| #18388 | 79 |