Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1056 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1056 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. #23774528 | C2 | semidirect |
| 3. #23762543 | C2 | semidirect |
| 4. #23762514 | C2 | semidirect |
| 5. #23762062 | C2 | semidirect |
| 6. #23761818 | C2 | semidirect |
| 7. C79×#3152 | C2 | semidirect |
| 19. #19098850 | C22 | semidirect |
| 20. #19098616 | C22 | semidirect |
| 21. #19098312 | C22 | semidirect |
| 23. #19098292 | C22 | semidirect |
| 26. C2×C4⋊Q8×C79 | C22 | semidirect |
| 28. #494×C79 | C22 | semidirect |
| 30. C4×M16×C79 | C22 | semidirect |
| 174. #3152 | D79 | semidirect |
| 179. C79 | #18715 | semidirect |
| 190. C2×C4⋊Q8 | C2×D79 | semidirect |
| 193. #494 | C2×D79 | semidirect |
| 199. C4×M16 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777805 | 2 |
| #23774528 | 2 |
| #23762543 | 2 |
| #23762514 | 2 |
| #23762062 | 2 |
| #23761818 | 2 |
| C79×#3152 | 2 |
| #18715 | 79 |