Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
930 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 1. #23765136 | C2 | semidirect |
| 2. #23765116 | C2 | semidirect |
| 3. #23765021 | C2 | semidirect |
| 4. #23763446 | C2 | semidirect |
| 6. C2×#14579101 | C22 | semidirect |
| 7. #19098601 | C22 | semidirect |
| 18. C2×#135×C79 | C4 | semidirect |
| 20. C22×D8×C79 | C4 | semidirect |
| 180. C79 | #12741 | semidirect |
| 186. C2×#135 | Dic79 | semidirect |
| 188. C22×D8 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765136 | 2 |
| #23765116 | 2 |
| #23765021 | 2 |
| #23763446 | 2 |
| C2×#576×C79 | 2 |
| #12741 | 79 |