Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
728 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 728 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. #23764345 | C2 | semidirect |
| 3. #23764330 | C2 | semidirect |
| 4. #23761999 | C2 | semidirect |
| 5. #23761926 | C2 | semidirect |
| 6. #23761811 | C2 | semidirect |
| 7. C79×#1552 | C2 | semidirect |
| 8. #19099317 | C4 | semidirect |
| 9. #19099311 | C4 | semidirect |
| 278. #1552 | D79 | semidirect |
| 282. C79 | #8511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777965 | 2 |
| #23764345 | 2 |
| #23764330 | 2 |
| #23761999 | 2 |
| #23761926 | 2 |
| #23761811 | 2 |
| C79×#1552 | 2 |
| #8511 | 79 |