Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
398 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 71 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×#19098362 | C2 | semidirect |
| 3. #23761568 | C2 | semidirect |
| 4. #23761566 | C2 | semidirect |
| 5. C2×#356×C79 | C2 | semidirect |
| 170. C2×#356 | D79 | semidirect |
| 173. C79 | #13590 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773857 | 2 |
| C2×#19098362 | 2 |
| #23761568 | 2 |
| #23761566 | 2 |
| C2×#356×C79 | 2 |
| #13590 | 79 |