Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
996 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 163 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. #23774783 | C2 | semidirect |
| 3. #23762625 | C2 | semidirect |
| 4. #23762576 | C2 | semidirect |
| 5. #23762135 | C2 | semidirect |
| 6. #23761852 | C2 | semidirect |
| 7. C79×#3131 | C2 | semidirect |
| 17. #19098840 | C22 | semidirect |
| 19. #19098765 | C22 | semidirect |
| 21. #19098587 | C22 | semidirect |
| 22. #19098312 | C22 | semidirect |
| 24. #19098292 | C22 | semidirect |
| 25. #533×C79 | C22 | semidirect |
| 28. #487×C79 | C22 | semidirect |
| 31. C2×C4×C8×C79 | C22 | semidirect |
| 182. #3131 | D79 | semidirect |
| 187. C79 | #18691 | semidirect |
| 195. #533 | C2×D79 | semidirect |
| 199. #487 | C2×D79 | semidirect |
| 208. C2×C4×C8 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777805 | 2 |
| #23774783 | 2 |
| #23762625 | 2 |
| #23762576 | 2 |
| #23762135 | 2 |
| #23761852 | 2 |
| C79×#3131 | 2 |
| #18691 | 79 |