Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
516 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×#19098376 | C2 | semidirect |
| 3. #23765115 | C2 | semidirect |
| 4. #23764310 | C2 | semidirect |
| 5. #23761495 | C2 | semidirect |
| 6. #23761489 | C2 | semidirect |
| 7. C79×#2948 | C2 | semidirect |
| 11. C2×#14579102 | C4 | semidirect |
| 32. C2×D632 | C2×C4 | semidirect |
| 40. C2×C79⋊C16 | C2×C4 | semidirect |
| 167. #2948 | D79 | semidirect |
| 173. C79 | #13017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579102 | 2 |
| C2×#19098376 | 2 |
| #23765115 | 2 |
| #23764310 | 2 |
| #23761495 | 2 |
| #23761489 | 2 |
| C79×#2948 | 2 |
| #13017 | 79 |