Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
560 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23770329 | C2 | semidirect |
| 2. #23764631 | C2 | semidirect |
| 4. #23761223 | C2 | semidirect |
| 5. #23761222 | C2 | semidirect |
| 6. #23761220 | C2 | semidirect |
| 7. C79×#2041 | C2 | semidirect |
| 234. #2041 | D79 | semidirect |
| 239. C79 | #7736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23770329 | 2 |
| #23764631 | 2 |
| #23764471 | 2 |
| #23761223 | 2 |
| #23761222 | 2 |
| #23761220 | 2 |
| C79×#2041 | 2 |
| #7736 | 79 |