Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
504 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23763515 | C2 | semidirect |
| 3. #23763252 | C2 | semidirect |
| 4. #23761223 | C2 | semidirect |
| 7. C79×#1271 | C2 | semidirect |
| 204. #1271 | D79 | semidirect |
| 207. C79 | #7614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765858 | 2 |
| #23763515 | 2 |
| #23763252 | 2 |
| #23761223 | 2 |
| #23761220 | 2 |
| C79×#1271 | 2 |
| #7614 | 79 |