Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
434 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#19098379 | C2 | semidirect |
| 4. #23765120 | C2 | semidirect |
| 5. #23765005 | C2 | semidirect |
| 6. #23763524 | C2 | semidirect |
| 24. #495×C79 | C4 | semidirect |
| 25. #494×C79 | C4 | semidirect |
| 176. C79 | #13216 | semidirect |
| 184. #495 | Dic79 | semidirect |
| 185. #494 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098379 | 2 |
| #23765136 | 2 |
| #23765128 | 2 |
| #23765120 | 2 |
| #23765005 | 2 |
| #23763524 | 2 |
| C79×#3156 | 2 |
| #13216 | 79 |