Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
198 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23761598 | C2 | semidirect |
| 4. #23761597 | C2 | semidirect |
| 5. C79×#1422 | C2 | semidirect |
| 78. #1422 | D79 | semidirect |
| 79. C79 | #13630 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M64×D79 | 2 |
| #23764995 | 2 |
| #23761598 | 2 |
| #23761597 | 2 |
| C79×#1422 | 2 |
| #13630 | 79 |