Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#19098830 | C2 | semidirect |
| 2. #23773066 | C2 | semidirect |
| 3. C2×#19098370 | C2 | semidirect |
| 4. C2×#19098364 | C2 | semidirect |
| 5. C2×#19098348 | C2 | semidirect |
| 6. #23761509 | C2 | semidirect |
| 7. C2×#509×C79 | C2 | semidirect |
| 54. #14579097 | D4 | semidirect |
| 74. C2×D8×C79 | D4 | semidirect |
| 79. M32×C79 | D4 | semidirect |
| 219. C2×#509 | D79 | semidirect |
| 226. C79 | #13307 | semidirect |
| 269. C2×D8 | C22⋊D79 | semidirect |
| 288. M32 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098830 | 2 |
| #23773066 | 2 |
| C2×#19098370 | 2 |
| C2×#19098364 | 2 |
| C2×#19098348 | 2 |
| #23761509 | 2 |
| C2×#509×C79 | 2 |
| #13307 | 79 |