Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
610 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23767874 | C2 | semidirect |
| 4. #23763490 | C2 | semidirect |
| 5. #23761973 | C2 | semidirect |
| 6. #23761246 | C2 | semidirect |
| 96. C22⋊Dic79 | SD16 | semidirect |
| 218. C79 | #9951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774157 | 2 |
| #23767874 | 2 |
| #23764237 | 2 |
| #23763490 | 2 |
| #23761973 | 2 |
| #23761246 | 2 |
| C2×#481×C79 | 2 |
| #9951 | 79 |