Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
462 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 462 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×#19098372 | C2 | semidirect |
| 3. #23765110 | C2 | semidirect |
| 4. #23761484 | C2 | semidirect |
| 5. C79×#1944 | C2 | semidirect |
| 51. #106×C79 | D4 | semidirect |
| 156. #1944 | D79 | semidirect |
| 158. C79 | #13410 | semidirect |
| 204. #106 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773846 | 2 |
| C2×#19098372 | 2 |
| #23765110 | 2 |
| #23761484 | 2 |
| C79×#1944 | 2 |
| #13410 | 79 |