Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
724 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23764357 | C2 | semidirect |
| 3. #23762095 | C2 | semidirect |
| 4. #23762001 | C2 | semidirect |
| 5. #23761923 | C2 | semidirect |
| 6. #23761814 | C2 | semidirect |
| 7. C79×#1980 | C2 | semidirect |
| 8. #19099313 | C4 | semidirect |
| 9. #19099307 | C4 | semidirect |
| 266. #1980 | D79 | semidirect |
| 271. C79 | #8513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777938 | 2 |
| #23764357 | 2 |
| #23762095 | 2 |
| #23762001 | 2 |
| #23761923 | 2 |
| #23761814 | 2 |
| C79×#1980 | 2 |
| #8513 | 79 |