Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23765186 | C2 | semidirect |
| 4. #23764183 | C2 | semidirect |
| 5. #23761496 | C2 | semidirect |
| 6. #23761488 | C2 | semidirect |
| 20. #19098376 | C4 | semidirect |
| 36. #14579101 | C2×C4 | semidirect |
| 39. #14579097 | C2×C4 | semidirect |
| 167. C79 | #12940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772252 | 2 |
| #23765186 | 2 |
| C2×#19098376 | 2 |
| #23764183 | 2 |
| #23761496 | 2 |
| #23761488 | 2 |
| C2×#357×C79 | 2 |
| #12940 | 79 |