Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1026 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 215 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. #23764196 | C2 | semidirect |
| 3. #23764016 | C2 | semidirect |
| 4. #23764010 | C2 | semidirect |
| 5. #23763694 | C2 | semidirect |
| 6. #23763310 | C2 | semidirect |
| 7. C79×#1779 | C2 | semidirect |
| 8. C22×#11929607 | C22 | semidirect |
| 11. C2×Dic79⋊C8 | C22 | semidirect |
| 14. C2×(C2×D79)⋊C8 | C22 | semidirect |
| 15. C2×#14579071 | C22 | semidirect |
| 20. #19098317 | C22 | semidirect |
| 21. #19098317 | C22 | semidirect |
| 77. C24×C79 | M16 | semidirect |
| 165. #1779 | D79 | semidirect |
| 166. C79 | #23309 | semidirect |
| 216. C24 | #11929607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579130 | 2 |
| #23764196 | 2 |
| #23764016 | 2 |
| #23764010 | 2 |
| #23763694 | 2 |
| #23763310 | 2 |
| C79×#1779 | 2 |
| #23309 | 79 |