Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
508 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23766117 | C2 | semidirect |
| 4. #23762071 | C2 | semidirect |
| 5. #23761258 | C2 | semidirect |
| 6. #23761228 | C2 | semidirect |
| 10. #19098966 | C4 | semidirect |
| 11. #19098909 | C4 | semidirect |
| 195. C79 | #9300 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774518 | 2 |
| #23766117 | 2 |
| #23764233 | 2 |
| #23762071 | 2 |
| #23761258 | 2 |
| #23761228 | 2 |
| C79×#1517 | 2 |
| #9300 | 79 |