Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
698 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23764934 | C2 | semidirect |
| 3. #23761221 | C2 | semidirect |
| 4. #23761220 | C2 | semidirect |
| 5. C79×#2094 | C2 | semidirect |
| 13. #19098318 | C22 | semidirect |
| 17. #384×C79 | C22 | semidirect |
| 18. #336×C79 | C22 | semidirect |
| 167. #2094 | D79 | semidirect |
| 170. C79 | #7822 | semidirect |
| 181. #384 | C2×D79 | semidirect |
| 183. #336 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769735 | 2 |
| #23764934 | 2 |
| #23761221 | 2 |
| #23761220 | 2 |
| C79×#2094 | 2 |
| #7822 | 79 |