Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
564 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 127 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. #23771990 | C2 | semidirect |
| 3. #23765117 | C2 | semidirect |
| 4. #23761506 | C2 | semidirect |
| 5. C2×#349×C79 | C2 | semidirect |
| 10. #19098816 | C4 | semidirect |
| 25. C2×D632 | C2×C4 | semidirect |
| 38. #14579095 | D4 | semidirect |
| 42. #14579093 | C2×C4 | semidirect |
| 160. C2×#349 | D79 | semidirect |
| 162. C79 | #12999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098816 | 2 |
| #23771990 | 2 |
| #23765117 | 2 |
| #23761506 | 2 |
| C2×#349×C79 | 2 |
| #12999 | 79 |