Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
416 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #23764188 | C2 | semidirect |
| 5. #23761516 | C2 | semidirect |
| 6. #23761487 | C2 | semidirect |
| 7. C79×#2155 | C2 | semidirect |
| 17. #19098377 | C4 | semidirect |
| 41. #14579097 | C2×C4 | semidirect |
| 50. M32×C79 | C2×C4 | semidirect |
| 139. #2155 | D79 | semidirect |
| 145. C79 | #12953 | semidirect |
| 181. M32 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772251 | 2 |
| C2×#19098377 | 2 |
| C2×#19098375 | 2 |
| #23764188 | 2 |
| #23761516 | 2 |
| #23761487 | 2 |
| C79×#2155 | 2 |
| #12953 | 79 |