Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
912 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 201 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. #23764192 | C2 | semidirect |
| 3. #23764009 | C2 | semidirect |
| 4. #23764003 | C2 | semidirect |
| 5. #23763694 | C2 | semidirect |
| 6. #23763312 | C2 | semidirect |
| 7. C79×#1780 | C2 | semidirect |
| 161. #1780 | D79 | semidirect |
| 162. C79 | #23312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766613 | 2 |
| #23764192 | 2 |
| #23764009 | 2 |
| #23764003 | 2 |
| #23763694 | 2 |
| #23763312 | 2 |
| C79×#1780 | 2 |
| #23312 | 79 |