Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1716 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1716 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#19099198 | C2 | semidirect |
| 2. #23773487 | C2 | semidirect |
| 3. #23762514 | C2 | semidirect |
| 4. #23762452 | C2 | semidirect |
| 5. #23762114 | C2 | semidirect |
| 6. #23761844 | C2 | semidirect |
| 7. C79×#3151 | C2 | semidirect |
| 16. #19098850 | C22 | semidirect |
| 17. #19098755 | C22 | semidirect |
| 20. #19098620 | C22 | semidirect |
| 21. #19098307 | C22 | semidirect |
| 22. #19098292 | C22 | semidirect |
| 24. #532×C79 | C22 | semidirect |
| 27. #493×C79 | C22 | semidirect |
| 28. #492×C79 | C22 | semidirect |
| 29. C4×M16×C79 | C22 | semidirect |
| 50. C4⋊(C79⋊C8) | C23 | semidirect |
| 62. C4⋊Q8×C79 | C23 | semidirect |
| 66. #127×C79 | C23 | semidirect |
| 72. C4×C8×C79 | C23 | semidirect |
| 153. D316 | AGL(1,ℤ/8) | semidirect |
| 185. #3151 | D79 | semidirect |
| 191. C79 | #18524 | semidirect |
| 197. #532 | C2×D79 | semidirect |
| 203. #493 | C2×D79 | semidirect |
| 204. #492 | C2×D79 | semidirect |
| 211. C4×M16 | C2×D79 | semidirect |
| 229. C4⋊Q8 | C22×D79 | semidirect |
| 233. #127 | C22×D79 | semidirect |
| 256. C4×C8 | C22×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099198 | 2 |
| #23773487 | 2 |
| #23762514 | 2 |
| #23762452 | 2 |
| #23762114 | 2 |
| #23761844 | 2 |
| C79×#3151 | 2 |
| #18524 | 79 |