Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
878 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23772439 | C2 | semidirect |
| 3. #23763320 | C2 | semidirect |
| 4. #23763320 | C2 | semidirect |
| 5. #23761736 | C2 | semidirect |
| 6. #23761306 | C2 | semidirect |
| 7. C79×#1305 | C2 | semidirect |
| 41. C2×#11929608 | D4 | semidirect |
| 67. C2×M16×C79 | D4 | semidirect |
| 190. C2×Dic79 | #100 | semidirect |
| 255. #1305 | D79 | semidirect |
| 256. C79 | #9504 | semidirect |
| 294. C2×M16 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772439 | 2 |
| #23766757 | 2 |
| #23763320 | 2 |
| #23761736 | 2 |
| #23761306 | 2 |
| C79×#1305 | 2 |
| #9504 | 79 |