Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
448 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 103 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×#19098320 | C2 | semidirect |
| 3. #23761389 | C2 | semidirect |
| 4. #23761386 | C2 | semidirect |
| 5. C2×#349×C79 | C2 | semidirect |
| 6. C2×#14579183 | C4 | semidirect |
| 9. #19098821 | C4 | semidirect |
| 11. #19098816 | C4 | semidirect |
| 15. #19098601 | C4 | semidirect |
| 26. C2×Dic316 | C2×C4 | semidirect |
| 28. C2×D632 | C2×C4 | semidirect |
| 46. #14579093 | C2×C4 | semidirect |
| 47. #14579093 | C2×C4 | semidirect |
| 194. C2×#349 | D79 | semidirect |
| 198. C79 | #11685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773009 | 2 |
| C2×#19098320 | 2 |
| #23761389 | 2 |
| #23761386 | 2 |
| C2×#349×C79 | 2 |
| #11685 | 79 |