Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
530 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23764318 | C2 | semidirect |
| 3. #23761998 | C2 | semidirect |
| 4. #23761946 | C2 | semidirect |
| 5. #23761264 | C2 | semidirect |
| 6. #23761256 | C2 | semidirect |
| 7. C79×#2337 | C2 | semidirect |
| 9. #19098953 | C4 | semidirect |
| 10. #19098922 | C4 | semidirect |
| 35. #14579161 | C2×C4 | semidirect |
| 36. #14579158 | C2×C4 | semidirect |
| 52. #14579072 | C2×C4 | semidirect |
| 223. #2337 | D79 | semidirect |
| 229. C79 | #9381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774387 | 2 |
| #23764318 | 2 |
| #23761998 | 2 |
| #23761946 | 2 |
| #23761264 | 2 |
| #23761256 | 2 |
| C79×#2337 | 2 |
| #9381 | 79 |