Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
822 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 147 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. #23766465 | C2 | semidirect |
| 3. #23764326 | C2 | semidirect |
| 4. #23761239 | C2 | semidirect |
| 5. C2×#331×C79 | C2 | semidirect |
| 10. #19098939 | C4 | semidirect |
| 29. #14579158 | C2×C4 | semidirect |
| 40. C4×C79⋊C8 | C2×C4 | semidirect |
| 73. C4⋊Dic79 | D8 | semidirect |
| 173. C2×#331 | D79 | semidirect |
| 175. C79 | #9061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098939 | 2 |
| #23766465 | 2 |
| #23764326 | 2 |
| #23761239 | 2 |
| C2×#331×C79 | 2 |
| #9061 | 79 |