Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1082 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1082 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 |
|---|---|---|
| 1. #23777805 | C2 | semidirect |
| 2. #23774778 | C2 | semidirect |
| 3. #23762543 | C2 | semidirect |
| 4. #23762514 | C2 | semidirect |
| 5. #23762481 | C2 | semidirect |
| 6. #23762452 | C2 | semidirect |
| 7. #23762135 | C2 | semidirect |
| 8. #23761852 | C2 | semidirect |
| 9. C79×#3147 | C2 | semidirect |
| 19. #19098850 | C22 | semidirect |
| 22. #19098755 | C22 | semidirect |
| 23. #19098587 | C22 | semidirect |
| 24. #19098312 | C22 | semidirect |
| 26. #19098292 | C22 | semidirect |
| 27. #19098292 | C22 | semidirect |
| 30. #532×C79 | C22 | semidirect |
| 32. #494×C79 | C22 | semidirect |
| 35. #492×C79 | C22 | semidirect |
| 36. C2×C4×C8×C79 | C22 | semidirect |
| 208. #3147 | D79 | semidirect |
| 215. C79 | #18686 | semidirect |
| 226. #532 | C2×D79 | semidirect |
| 228. #494 | C2×D79 | semidirect |
| 231. #492 | C2×D79 | semidirect |
| 238. 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 |
| #23774778 | 2 |
| #23762543 | 2 |
| #23762514 | 2 |
| #23762481 | 2 |
| #23762452 | 2 |
| #23762135 | 2 |
| #23761852 | 2 |
| C79×#3147 | 2 |
| #18686 | 79 |