Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
416 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23765174 | C2 | semidirect |
| 5. #23761514 | C2 | semidirect |
| 6. #23761486 | C2 | semidirect |
| 7. C79×#1953 | C2 | semidirect |
| 18. #19098375 | C4 | semidirect |
| 38. #14579101 | C2×C4 | semidirect |
| 53. #108×C79 | C2×C4 | semidirect |
| 142. #1953 | D79 | semidirect |
| 145. C79 | #12953 | semidirect |
| 188. #108 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772253 | 2 |
| #23765174 | 2 |
| C2×#19098375 | 2 |
| #23761514 | 2 |
| #23761486 | 2 |
| C79×#1953 | 2 |
| #12953 | 79 |