Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
484 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#19098362 | C2 | semidirect |
| 3. #23761555 | C2 | direct (N × H) |
| 4. C2×#333×C79 | C2 | semidirect |
| 15. #19098362 | C22 | semidirect |
| 19. #333×C79 | C22 | semidirect |
| 168. C2×C79 | #1405 | semidirect |
| 173. C2×#333 | D79 | semidirect |
| 175. C79 | C2×#1405 | semidirect |
| 190. #333 | C2×D79 | semidirect |
| 339. C2 | #23761555 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098745 | 2 |
| C2×#19098362 | 2 |
| #23761555 | 2 |
| C2×#333×C79 | 2 |
| C2×#1405 | 79 |