Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
574 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23761727 | C2 | semidirect |
| 3. #23761399 | C2 | semidirect |
| 4. #23761396 | C2 | semidirect |
| 5. C79×#1819 | C2 | semidirect |
| 6. C2×#14579135 | C4 | semidirect |
| 9. #19098488 | C4 | semidirect |
| 13. #19098472 | C4 | semidirect |
| 16. #19098423 | C4 | semidirect |
| 225. #1819 | D79 | semidirect |
| 229. C79 | #11799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769134 | 2 |
| #23761727 | 2 |
| #23761399 | 2 |
| #23761396 | 2 |
| C79×#1819 | 2 |
| #11799 | 79 |