Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
672 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23762106 | C2 | semidirect |
| 3. #23761977 | C2 | semidirect |
| 4. #23761952 | C2 | semidirect |
| 5. #23761948 | C2 | semidirect |
| 6. #23761872 | C2 | semidirect |
| 7. C79×#1535 | C2 | semidirect |
| 10. #19099278 | C4 | semidirect |
| 11. #19099273 | C4 | semidirect |
| 14. Q8×D316 | C4 | semidirect |
| 16. #19099217 | C4 | semidirect |
| 272. #1535 | D79 | semidirect |
| 277. C79 | #8502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777791 | 2 |
| #23762106 | 2 |
| #23761977 | 2 |
| #23761952 | 2 |
| #23761948 | 2 |
| #23761872 | 2 |
| C79×#1535 | 2 |
| #8502 | 79 |