Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
364 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23773923 | C2 | semidirect |
| 5. #23761514 | C2 | semidirect |
| 6. #23761479 | C2 | semidirect |
| 7. C79×#1389 | C2 | semidirect |
| 28. C2×Dic316 | Q8 | semidirect |
| 30. C2×D632 | Q8 | semidirect |
| 154. #1389 | D79 | semidirect |
| 156. C79 | #13373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773923 | 2 |
| #23765137 | 2 |
| #23765135 | 2 |
| #23764291 | 2 |
| #23761514 | 2 |
| #23761479 | 2 |
| C79×#1389 | 2 |
| #13373 | 79 |