Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
450 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 85 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. C22⋊C16×D79 | C2 | semidirect |
| 3. #341×D79 | C2 | semidirect |
| 4. #23761418 | C2 | semidirect |
| 5. #23761416 | C2 | semidirect |
| 6. #23761414 | C2 | semidirect |
| 7. C79×#1350 | C2 | semidirect |
| 186. #1350 | D79 | semidirect |
| 189. C79 | #11709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772983 | 2 |
| C22⋊C16×D79 | 2 |
| #341×D79 | 2 |
| #23761418 | 2 |
| #23761416 | 2 |
| #23761414 | 2 |
| C79×#1350 | 2 |
| #11709 | 79 |