Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
684 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 161 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. #23763255 | C2 | semidirect |
| 4. #23761283 | C2 | semidirect |
| 5. C79×#1296 | C2 | semidirect |
| 15. #19098306 | C4 | semidirect |
| 35. C4⋊(C79⋊C8) | C2×C4 | semidirect |
| 42. C4⋊C8×C79 | C2×C4 | semidirect |
| 147. #1296 | D79 | semidirect |
| 148. C79 | #8231 | semidirect |
| 184. C4⋊C8 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765962 | 2 |
| #23763255 | 2 |
| C2×#19098306 | 2 |
| #23761283 | 2 |
| C79×#1296 | 2 |
| #8231 | 79 |