Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
418 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23764964 | C2 | semidirect |
| 3. #23764963 | C2 | semidirect |
| 5. #23761224 | C2 | semidirect |
| 7. C79×#1271 | C2 | semidirect |
| 192. #1271 | D79 | semidirect |
| 194. C79 | #7824 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23770329 | 2 |
| #23764964 | 2 |
| #23764963 | 2 |
| #23764932 | 2 |
| #23761224 | 2 |
| #23761220 | 2 |
| C79×#1271 | 2 |
| #7824 | 79 |