Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
564 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 1. #23774138 | C2 | semidirect |
| 2. #23765614 | C2 | semidirect |
| 3. #23765571 | C2 | semidirect |
| 4. #23765476 | C2 | semidirect |
| 5. #23765346 | C2 | semidirect |
| 6. #23765298 | C2 | semidirect |
| 7. #23765212 | C2 | semidirect |
| 8. C79×#2956 | C2 | semidirect |
| 11. #19098961 | C22 | semidirect |
| 12. #19098940 | C22 | semidirect |
| 17. #19098676 | C22 | semidirect |
| 18. #19098387 | C22 | semidirect |
| 19. #19098384 | C22 | semidirect |
| 20. #19098375 | C22 | semidirect |
| 23. #19098341 | C22 | semidirect |
| 96. Q16×C79 | #41 | semidirect |
| 100. D8×C79 | #41 | semidirect |
| 171. #2956 | D79 | semidirect |
| 178. C79 | #33688 | semidirect |
| 259. Q16 | #11929624 | semidirect |
| 265. D8 | #11929624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774138 | 2 |
| #23765614 | 2 |
| #23765571 | 2 |
| #23765476 | 2 |
| #23765346 | 2 |
| #23765298 | 2 |
| #23765212 | 2 |
| C79×#2956 | 2 |
| #33688 | 79 |