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. #23772385 | C2 | semidirect |
| 3. #23762029 | C2 | semidirect |
| 4. #23761844 | C2 | semidirect |
| 5. #23761740 | C2 | semidirect |
| 6. C79⋊#1308 | C2 | semidirect |
| 7. C79×#1291 | C2 | semidirect |
| 211. #1291 | 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 |
|---|---|
| #23773540 | 2 |
| #23772385 | 2 |
| #23762029 | 2 |
| #23761844 | 2 |
| #23761740 | 2 |
| C79⋊#1308 | 2 |
| C79×#1291 | 2 |
| #9532 | 79 |