Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
2310 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2310 conjugacy classes of subgroups — too many to draw. Only its 747 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. C22×#14579153 | C2 | semidirect |
| 3. C2×#19098918 | C2 | direct (N × H) |
| 4. C22×#14579086 | C2 | semidirect |
| 6. C22×C4×C8×C79 | C2 | semidirect |
| 10. C2×#14579153 | C22 | semidirect |
| 16. #19098918 | C22 | direct (N × H) |
| 17. C2×#14579086 | C22 | semidirect |
| 21. C2×C4×C8×C79 | C22 | semidirect |
| 32. #14579153 | C23 | semidirect |
| 39. #14579086 | C23 | semidirect |
| 47. C4×C8×C79 | C23 | semidirect |
| 99. C22×C79 | #488 | semidirect |
| 112. C2×C79 | C2×#488 | semidirect |
| 121. C22×C4×C8 | D79 | semidirect |
| 122. C79 | C22×#488 | semidirect |
| 137. C2×C4×C8 | C2×D79 | semidirect |
| 163. C4×C8 | C22×D79 | semidirect |
| 218. C22 | #19098918 | direct (N × H) |
| 228. C2 | C2×#19098918 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579153 | 2 |
| C22×#14579149 | 2 |
| C2×#19098918 | 2 |
| C22×#14579086 | 2 |
| C22×#14579083 | 2 |
| C22×C4×C8×C79 | 2 |
| C22×#488 | 79 |