Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
444 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23772380 | C2 | semidirect |
| 3. #23762029 | C2 | semidirect |
| 4. #23761843 | C2 | semidirect |
| 5. C79⋊#1308 | C2 | semidirect |
| 6. #23761271 | C2 | semidirect |
| 7. C79×#1466 | C2 | semidirect |
| 209. #1466 | D79 | semidirect |
| 212. C79 | #9532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773538 | 2 |
| #23772380 | 2 |
| #23762029 | 2 |
| #23761843 | 2 |
| C79⋊#1308 | 2 |
| #23761271 | 2 |
| C79×#1466 | 2 |
| #9532 | 79 |