Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
894 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23772660 | C2 | semidirect |
| 2. #23768558 | C2 | semidirect |
| 3. #23763344 | C2 | semidirect |
| 4. #23761932 | C2 | semidirect |
| 5. #23761727 | C2 | semidirect |
| 6. #23761252 | C2 | semidirect |
| 33. C22×Dic158 | D4 | semidirect |
| 43. C2×C4⋊Dic79 | D4 | semidirect |
| 49. C2×C4×Dic79 | D4 | semidirect |
| 56. C22⋊(C79⋊C8) | D4 | semidirect |
| 281. C79 | #9942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772660 | 2 |
| #23768558 | 2 |
| #23763344 | 2 |
| #23761932 | 2 |
| #23761727 | 2 |
| #23761252 | 2 |
| C79×#2404 | 2 |
| #9942 | 79 |