Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
612 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #23764344 | C2 | semidirect |
| 4. #23761913 | C2 | semidirect |
| 5. #23761294 | C2 | semidirect |
| 6. #23761255 | C2 | semidirect |
| 11. #19098843 | C4 | semidirect |
| 12. #19098768 | C4 | semidirect |
| 31. #14579161 | C2×C4 | semidirect |
| 32. #14579161 | C2×C4 | semidirect |
| 46. C4⋊(C79⋊C8) | C2×C4 | semidirect |
| 193. C79 | #9323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773499 | 2 |
| #23765761 | 2 |
| #23764344 | 2 |
| #23761913 | 2 |
| #23761294 | 2 |
| #23761255 | 2 |
| C79×#1490 | 2 |
| #9323 | 79 |