Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
470 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 470 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. #23763429 | C2 | semidirect |
| 3. #23761410 | C2 | semidirect |
| 4. C2×C22⋊C16×C79 | C2 | semidirect |
| 5. C22×D632 | C4 | semidirect |
| 9. #19098799 | C4 | semidirect |
| 12. C2×#14579095 | C4 | semidirect |
| 15. #19098326 | C22 | semidirect |
| 19. C22⋊C16×C79 | C22 | semidirect |
| 162. C2×C22⋊C16 | D79 | semidirect |
| 165. C79 | #11886 | semidirect |
| 179. C22⋊C16 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098799 | 2 |
| #23763429 | 2 |
| #23761410 | 2 |
| C2×C22⋊C16×C79 | 2 |
| #11886 | 79 |