Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
492 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23764725 | C2 | semidirect |
| 4. #23761223 | C2 | semidirect |
| 5. #23761222 | C2 | semidirect |
| 7. C79×#2057 | C2 | semidirect |
| 205. #2057 | D79 | semidirect |
| 210. C79 | #7751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23770329 | 2 |
| #23764725 | 2 |
| #23764483 | 2 |
| #23761223 | 2 |
| #23761222 | 2 |
| #23761220 | 2 |
| C79×#2057 | 2 |
| #7751 | 79 |