Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
624 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 91 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. #23772471 | C2 | semidirect |
| 3. #23763349 | C2 | semidirect |
| 4. #23761522 | C2 | semidirect |
| 5. C79×#2132 | C2 | semidirect |
| 196. #2132 | D79 | semidirect |
| 199. C79 | #13052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772748 | 2 |
| #23772471 | 2 |
| #23763349 | 2 |
| #23761522 | 2 |
| C79×#2132 | 2 |
| #13052 | 79 |