Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
672 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #23765054 | C2 | semidirect |
| 5. #23761528 | C2 | semidirect |
| 6. #23761520 | C2 | semidirect |
| 7. C79×#2129 | C2 | semidirect |
| 9. C2×#14579192 | C4 | semidirect |
| 10. C22×#11929611 | C4 | semidirect |
| 18. #19098567 | C4 | semidirect |
| 19. #19098557 | C4 | semidirect |
| 50. C2×#11929608 | C2×C4 | semidirect |
| 51. C22×C79⋊C8 | C2×C4 | semidirect |
| 70. C22×Q8×C79 | C2×C4 | semidirect |
| 79. #117×C79 | C2×C4 | semidirect |
| 254. #2129 | D79 | semidirect |
| 259. C79 | #13100 | semidirect |
| 290. C22×Q8 | C4×D79 | semidirect |
| 317. #117 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772675 | 2 |
| #23771859 | 2 |
| #23765054 | 2 |
| #23763368 | 2 |
| #23761528 | 2 |
| #23761520 | 2 |
| C79×#2129 | 2 |
| #13100 | 79 |