Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
686 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 686 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. #23766158 | C2 | semidirect |
| 4. #23761933 | C2 | semidirect |
| 5. #23761309 | C2 | semidirect |
| 6. #23761254 | C2 | semidirect |
| 27. #451×C79 | C4 | semidirect |
| 28. #450×C79 | C4 | semidirect |
| 274. C79 | #9524 | semidirect |
| 279. #451 | Dic79 | semidirect |
| 280. #450 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766158 | 2 |
| #23763344 | 2 |
| #23763318 | 2 |
| #23761933 | 2 |
| #23761309 | 2 |
| #23761254 | 2 |
| C79×#3007 | 2 |
| #9524 | 79 |