Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
494 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 494 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. #23772276 | C2 | semidirect |
| 3. C2×#19098365 | C2 | semidirect |
| 4. #23764308 | C2 | semidirect |
| 5. #23761510 | C2 | semidirect |
| 6. #23761488 | C2 | semidirect |
| 7. C2×#359×C79 | C2 | semidirect |
| 11. #19098998 | C4 | semidirect |
| 34. C2×D632 | C2×C4 | semidirect |
| 46. #14579101 | C2×C4 | semidirect |
| 191. C2×#359 | D79 | semidirect |
| 196. C79 | #13022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098998 | 2 |
| #23772276 | 2 |
| C2×#19098365 | 2 |
| #23764308 | 2 |
| #23761510 | 2 |
| #23761488 | 2 |
| C2×#359×C79 | 2 |
| #13022 | 79 |