Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1310 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1310 conjugacy classes of subgroups — too many to draw. Only its 167 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. C2×#19099189 | C2 | semidirect |
| 2. #23772660 | C2 | semidirect |
| 3. #23762356 | C2 | semidirect |
| 4. #23762322 | C2 | semidirect |
| 5. #23761932 | C2 | semidirect |
| 6. #23761727 | C2 | semidirect |
| 18. #19098719 | C22 | semidirect |
| 19. #19098714 | C22 | semidirect |
| 22. #19098299 | C22 | semidirect |
| 33. C22×Dic158 | D4 | semidirect |
| 44. #14579140 | D4 | semidirect |
| 51. C2×C4⋊Dic79 | D4 | semidirect |
| 171. C23×C79 | #137 | semidirect |
| 253. C79 | #18133 | semidirect |
| 417. C23 | #14579191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099189 | 2 |
| #23772660 | 2 |
| #23762356 | 2 |
| #23762322 | 2 |
| #23761932 | 2 |
| #23761727 | 2 |
| C79×#2404 | 2 |
| #18133 | 79 |