Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
214 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 3. #23761536 | C2 | semidirect |
| 4. #23761535 | C2 | semidirect |
| 5. C79×#1398 | C2 | semidirect |
| 10. #19098396 | C4 | semidirect |
| 11. C32×D79 | C4 | semidirect |
| 78. #1398 | D79 | semidirect |
| 79. C79 | #13551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M64×D79 | 2 |
| #23764998 | 2 |
| #23761536 | 2 |
| #23761535 | 2 |
| C79×#1398 | 2 |
| #13551 | 79 |