Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1056 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 179 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. #23774525 | C2 | semidirect |
| 2. #23773860 | C2 | semidirect |
| 3. #23762545 | C2 | semidirect |
| 4. #23762516 | C2 | semidirect |
| 5. #23762062 | C2 | semidirect |
| 6. #23761817 | C2 | semidirect |
| 9. C2×#14579161 | C22 | semidirect |
| 12. #19098942 | C22 | semidirect |
| 16. #19098853 | C22 | semidirect |
| 17. #19098616 | C22 | semidirect |
| 18. C4×#11929608 | C22 | semidirect |
| 19. #19098312 | C22 | semidirect |
| 21. D4⋊(C79⋊C8) | C22 | semidirect |
| 179. C79 | #18715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774525 | 2 |
| #23773860 | 2 |
| #23762545 | 2 |
| #23762516 | 2 |
| #23762062 | 2 |
| #23761817 | 2 |
| C79×#3549 | 2 |
| #18715 | 79 |