Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
416 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23765173 | C2 | semidirect |
| 4. #23764191 | C2 | semidirect |
| 5. #23761514 | C2 | semidirect |
| 6. #23761487 | C2 | semidirect |
| 23. #361×C79 | C4 | semidirect |
| 52. M32×C79 | C2×C4 | semidirect |
| 55. #108×C79 | C2×C4 | semidirect |
| 145. C79 | #12953 | semidirect |
| 160. #361 | Dic79 | semidirect |
| 181. M32 | C2×Dic79 | semidirect |
| 188. #108 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772252 | 2 |
| #23765173 | 2 |
| C2×#19098376 | 2 |
| #23764191 | 2 |
| #23761514 | 2 |
| #23761487 | 2 |
| C2×#361×C79 | 2 |
| #12953 | 79 |