Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
594 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #23767886 | C2 | semidirect |
| 5. #23763484 | C2 | semidirect |
| 6. #23761246 | C2 | semidirect |
| 7. C79×#1520 | C2 | semidirect |
| 217. #1520 | D79 | semidirect |
| 219. C79 | #9953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774153 | 2 |
| C2×#19098877 | 2 |
| #23767886 | 2 |
| #23764235 | 2 |
| #23763484 | 2 |
| #23761246 | 2 |
| C79×#1520 | 2 |
| #9953 | 79 |