Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
938 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 938 conjugacy classes of subgroups — too many to draw. Only its 155 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. #23774399 | C2 | semidirect |
| 3. #23762715 | C2 | semidirect |
| 4. #23762027 | C2 | semidirect |
| 5. #23761997 | C2 | semidirect |
| 6. C79×#3166 | C2 | semidirect |
| 14. #19098955 | C22 | semidirect |
| 15. #19098925 | C22 | semidirect |
| 20. #19098305 | C22 | semidirect |
| 21. #19098302 | C22 | semidirect |
| 24. #501×C79 | C22 | semidirect |
| 154. #3166 | D79 | semidirect |
| 158. C79 | #19006 | semidirect |
| 168. #501 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099311 | 2 |
| #23774399 | 2 |
| #23762715 | 2 |
| #23762027 | 2 |
| #23761997 | 2 |
| C79×#3166 | 2 |
| #19006 | 79 |