Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
500 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23761734 | C2 | semidirect |
| 3. #23761423 | C2 | semidirect |
| 5. C79×#1740 | C2 | semidirect |
| 6. C2×C4×D316 | C4 | semidirect |
| 8. #19098502 | C4 | semidirect |
| 10. #19098480 | C4 | semidirect |
| 16. #19098431 | C4 | semidirect |
| 196. #1740 | D79 | semidirect |
| 200. C79 | #11754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23768966 | 2 |
| #23761734 | 2 |
| #23761423 | 2 |
| #23761396 | 2 |
| C79×#1740 | 2 |
| #11754 | 79 |