Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
456 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23772476 | C2 | semidirect |
| 2. #23761908 | C2 | semidirect |
| 3. #23761908 | C2 | semidirect |
| 4. #23761869 | C2 | semidirect |
| 5. #23761262 | C2 | semidirect |
| 6. #23761228 | C2 | semidirect |
| 22. #493×C79 | C4 | semidirect |
| 23. #492×C79 | C4 | semidirect |
| 24. #487×C79 | C4 | semidirect |
| 25. #486×C79 | C4 | semidirect |
| 186. C79 | #9281 | semidirect |
| 189. #493 | Dic79 | semidirect |
| 190. #492 | Dic79 | semidirect |
| 191. #487 | Dic79 | semidirect |
| 192. #486 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772476 | 2 |
| #23761908 | 2 |
| #23761869 | 2 |
| #23761262 | 2 |
| #23761228 | 2 |
| C79×#3207 | 2 |
| #9281 | 79 |