Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
500 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23764957 | C2 | semidirect |
| 3. #23764804 | C2 | semidirect |
| 4. #23761222 | C2 | semidirect |
| 5. #23761221 | C2 | semidirect |
| 6. #23761220 | C2 | semidirect |
| 7. C79×#2071 | C2 | semidirect |
| 218. #2071 | D79 | semidirect |
| 222. C79 | #7795 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769763 | 2 |
| #23764957 | 2 |
| #23764804 | 2 |
| #23761222 | 2 |
| #23761221 | 2 |
| #23761220 | 2 |
| C79×#2071 | 2 |
| #7795 | 79 |