Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
982 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 982 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23769216 | C2 | semidirect |
| 4. C2×#19098301 | C2 | semidirect |
| 5. C2×#19098288 | C2 | semidirect |
| 6. #23761278 | C2 | semidirect |
| 101. C22×Dic79 | SD16 | semidirect |
| 286. C79 | #9923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098714 | 2 |
| #23769216 | 2 |
| C2×#19098477 | 2 |
| C2×#19098301 | 2 |
| C2×#19098288 | 2 |
| #23761278 | 2 |
| C79×#1786 | 2 |
| #9923 | 79 |