Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
536 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23763438 | C2 | semidirect |
| 2. #23763176 | C2 | semidirect |
| 3. #23761916 | C2 | semidirect |
| 4. #23761760 | C2 | semidirect |
| 15. C22×D8×C79 | C4 | semidirect |
| 22. C2×#107×C79 | C4 | semidirect |
| 23. C2×#102×C79 | C4 | semidirect |
| 176. C79 | #9818 | semidirect |
| 177. C22×D8 | Dic79 | semidirect |
| 185. C2×#107 | Dic79 | semidirect |
| 186. C2×#102 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763438 | 2 |
| #23763176 | 2 |
| #23761916 | 2 |
| #23761760 | 2 |
| C2×#466×C79 | 2 |
| #9818 | 79 |