Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
530 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23764228 | C2 | semidirect |
| 3. #23762156 | C2 | semidirect |
| 4. #23761852 | C2 | semidirect |
| 5. C4×#97×C79 | C2 | semidirect |
| 7. #19098968 | C4 | semidirect |
| 8. #19098940 | C4 | semidirect |
| 9. #19098910 | C4 | semidirect |
| 102. C8×C79 | #104 | semidirect |
| 127. C4×#97 | D79 | semidirect |
| 130. C79 | #9849 | semidirect |
| 228. C8 | #14579089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773979 | 2 |
| #23764228 | 2 |
| #23762156 | 2 |
| #23761852 | 2 |
| C4×#97×C79 | 2 |
| #9849 | 79 |