Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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×#19098994 | C2 | semidirect |
| 2. #23773829 | C2 | semidirect |
| 3. #23773827 | C2 | semidirect |
| 4. #23765660 | C2 | semidirect |
| 5. #23765656 | C2 | semidirect |
| 6. #23765652 | C2 | semidirect |
| 7. #23765649 | C2 | semidirect |
| 8. C4×C16×D79 | C2 | semidirect |
| 9. C79×#2248 | C2 | semidirect |
| 65. C16×D79 | D4 | semidirect |
| 159. C4×C79 | #508 | semidirect |
| 176. #2248 | D79 | semidirect |
| 180. C79 | #33713 | semidirect |
| 333. C4 | #19098994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098994 | 2 |
| #23773829 | 2 |
| #23773827 | 2 |
| #23765660 | 2 |
| #23765656 | 2 |
| #23765652 | 2 |
| #23765649 | 2 |
| C4×C16×D79 | 2 |
| C79×#2248 | 2 |
| #33713 | 79 |