Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
184 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23765693 | C2 | semidirect |
| 3. #23761597 | C2 | semidirect |
| 4. #23761543 | C2 | semidirect |
| 5. #23761542 | C2 | semidirect |
| 6. #23761533 | C2 | semidirect |
| 7. C79×#2258 | C2 | semidirect |
| 93. #2258 | D79 | semidirect |
| 99. C79 | #13648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765693 | 2 |
| #23765235 | 2 |
| #23761597 | 2 |
| #23761543 | 2 |
| #23761542 | 2 |
| #23761533 | 2 |
| C79×#2258 | 2 |
| #13648 | 79 |