Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
634 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 634 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. #23774707 | C2 | semidirect |
| 2. #23772866 | C2 | semidirect |
| 3. #23772860 | C2 | semidirect |
| 4. #23764194 | C2 | semidirect |
| 5. #23761852 | C2 | semidirect |
| 6. #23761274 | C2 | semidirect |
| 7. C79×#1492 | C2 | semidirect |
| 101. C2×D316 | D8 | semidirect |
| 254. #1492 | D79 | semidirect |
| 256. C79 | #10254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774707 | 2 |
| #23772866 | 2 |
| #23772860 | 2 |
| #23764194 | 2 |
| #23761852 | 2 |
| #23761274 | 2 |
| C79×#1492 | 2 |
| #10254 | 79 |