Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
822 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 155 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. #23764327 | C2 | semidirect |
| 3. C2×#19098307 | C2 | semidirect |
| 4. #23761241 | C2 | semidirect |
| 5. C79×#2366 | C2 | semidirect |
| 9. #19098939 | C4 | semidirect |
| 29. #14579158 | C2×C4 | semidirect |
| 35. C4×C79⋊C8 | C2×C4 | semidirect |
| 89. C4⋊C4×C79 | D8 | semidirect |
| 171. #2366 | D79 | semidirect |
| 175. C79 | #9061 | semidirect |
| 259. C4⋊C4 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098939 | 2 |
| #23764327 | 2 |
| C2×#19098307 | 2 |
| #23761241 | 2 |
| C79×#2366 | 2 |
| #9061 | 79 |