Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1200 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 171 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×#19098745 | C2 | semidirect |
| 2. C2×#19098735 | C2 | semidirect |
| 3. #23765426 | C2 | direct (N × H) |
| 4. C2×#19098362 | C2 | semidirect |
| 5. C2×#19098360 | C2 | semidirect |
| 6. C2×#555×C79 | C2 | semidirect |
| 11. #19098745 | C22 | semidirect |
| 13. #19098735 | C22 | semidirect |
| 18. #19098362 | C22 | semidirect |
| 19. #19098360 | C22 | semidirect |
| 22. #555×C79 | C22 | semidirect |
| 224. C2×C79 | #2204 | semidirect |
| 227. C2×#555 | D79 | semidirect |
| 233. C79 | C2×#2204 | semidirect |
| 239. #555 | C2×D79 | semidirect |
| 451. C2 | #23765426 | 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×#19098735 | 2 |
| #23765426 | 2 |
| C2×#19098362 | 2 |
| C2×#19098360 | 2 |
| C2×#555×C79 | 2 |
| C2×#2204 | 79 |