Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
466 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19098377 | C2 | semidirect |
| 3. #23765128 | C2 | semidirect |
| 4. #23765115 | C2 | semidirect |
| 5. #23765004 | C2 | semidirect |
| 6. #23763523 | C2 | semidirect |
| 7. C79×#2145 | C2 | semidirect |
| 13. #19098948 | C4 | semidirect |
| 14. #19098938 | C4 | semidirect |
| 47. C2×C79⋊C16 | D4 | semidirect |
| 63. M32×C79 | D4 | semidirect |
| 177. #2145 | D79 | semidirect |
| 182. C79 | #13215 | semidirect |
| 233. M32 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773887 | 2 |
| C2×#19098377 | 2 |
| #23765128 | 2 |
| #23765115 | 2 |
| #23765004 | 2 |
| #23763523 | 2 |
| C79×#2145 | 2 |
| #13215 | 79 |