Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
422 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 422 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. #23764942 | C2 | semidirect |
| 3. #23764808 | C2 | semidirect |
| 5. #23761225 | C2 | semidirect |
| 7. C79×#1272 | C2 | semidirect |
| 198. #1272 | D79 | semidirect |
| 200. C79 | #7804 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771344 | 2 |
| #23764942 | 2 |
| #23764808 | 2 |
| #23764805 | 2 |
| #23761225 | 2 |
| #23761220 | 2 |
| C79×#1272 | 2 |
| #7804 | 79 |