Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
526 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 101 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. #23774742 | C2 | semidirect |
| 5. #23761856 | C2 | semidirect |
| 6. #23761274 | C2 | semidirect |
| 7. C79×#1493 | C2 | semidirect |
| 91. C2×D316 | Q16 | semidirect |
| 216. #1493 | D79 | semidirect |
| 218. C79 | #10258 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774742 | 2 |
| #23773199 | 2 |
| #23773193 | 2 |
| #23764194 | 2 |
| #23761856 | 2 |
| #23761274 | 2 |
| C79×#1493 | 2 |
| #10258 | 79 |