Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
504 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23772454 | C2 | semidirect |
| 3. #23761905 | C2 | semidirect |
| 4. C2×#19098298 | C2 | semidirect |
| 5. #23761761 | C2 | semidirect |
| 6. #23761242 | C2 | semidirect |
| 7. C79×#1298 | C2 | semidirect |
| 10. #19098899 | C4 | semidirect |
| 12. #19098882 | C4 | semidirect |
| 15. #19098716 | C4 | semidirect |
| 17. #19098699 | C4 | semidirect |
| 251. #1298 | D79 | semidirect |
| 253. C79 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774167 | 2 |
| #23772454 | 2 |
| #23761905 | 2 |
| C2×#19098298 | 2 |
| #23761761 | 2 |
| #23761242 | 2 |
| C79×#1298 | 2 |
| #9264 | 79 |