Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
290 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 79 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×#19098396 | C2 | semidirect |
| 3. #368×D79 | C2 | semidirect |
| 4. #23761585 | C2 | semidirect |
| 5. #23761584 | C2 | semidirect |
| 6. #23761583 | C2 | semidirect |
| 7. C79×#1417 | C2 | semidirect |
| 21. C2×C79⋊C32 | C22 | semidirect |
| 22. #19098393 | C22 | semidirect |
| 25. C2×C32×C79 | C22 | semidirect |
| 26. #368×C79 | C22 | semidirect |
| 150. #1417 | D79 | semidirect |
| 151. C79 | #13620 | semidirect |
| 167. C2×C32 | C2×D79 | semidirect |
| 170. #368 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #508×D79 | 2 |
| C2×#19098396 | 2 |
| #368×D79 | 2 |
| #23761585 | 2 |
| #23761584 | 2 |
| #23761583 | 2 |
| C79×#1417 | 2 |
| #13620 | 79 |