Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
540 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 540 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 |
|---|---|---|
| 2. C2×#19098375 | C2 | semidirect |
| 3. #23765115 | C2 | semidirect |
| 4. #23761482 | C2 | semidirect |
| 5. C79×#1945 | C2 | semidirect |
| 40. #107×C79 | D4 | semidirect |
| 122. #1945 | D79 | semidirect |
| 124. C79 | #13413 | semidirect |
| 159. #107 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098940 | 2 |
| C2×#19098375 | 2 |
| #23765115 | 2 |
| #23761482 | 2 |
| C79×#1945 | 2 |
| #13413 | 79 |