Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
476 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 69 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. #23763387 | C2 | semidirect |
| 3. #23761735 | C2 | semidirect |
| 4. #23761422 | C2 | semidirect |
| 5. #23761420 | C2 | semidirect |
| 6. #23761397 | C2 | semidirect |
| 7. C79×#1343 | C2 | semidirect |
| 8. C2×#14579148 | C4 | semidirect |
| 13. #19098476 | C4 | semidirect |
| 16. #19098471 | C4 | semidirect |
| 19. #19098430 | C4 | semidirect |
| 227. #1343 | D79 | semidirect |
| 228. C79 | #11825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769257 | 2 |
| #23763387 | 2 |
| #23761735 | 2 |
| #23761422 | 2 |
| #23761420 | 2 |
| #23761397 | 2 |
| C79×#1343 | 2 |
| #11825 | 79 |