Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
344 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. #23765602 | C2 | semidirect |
| 4. #23761413 | C2 | semidirect |
| 5. #23761412 | C2 | semidirect |
| 7. C79×#2236 | C2 | semidirect |
| 166. #2236 | D79 | semidirect |
| 171. C79 | #12282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774171 | 2 |
| #23765602 | 2 |
| #23764829 | 2 |
| #23761413 | 2 |
| #23761412 | 2 |
| #23761323 | 2 |
| C79×#2236 | 2 |
| #12282 | 79 |