Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
808 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 171 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. #23762728 | C2 | semidirect |
| 4. #23762702 | C2 | semidirect |
| 5. #23762027 | C2 | semidirect |
| 6. #23762002 | C2 | semidirect |
| 7. C2×#564×C79 | C2 | semidirect |
| 147. C2×#564 | D79 | semidirect |
| 154. C79 | #19003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774590 | 2 |
| #23773803 | 2 |
| #23762728 | 2 |
| #23762702 | 2 |
| #23762027 | 2 |
| #23762002 | 2 |
| C2×#564×C79 | 2 |
| #19003 | 79 |