Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
930 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 219 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×#14579105 | C2 | semidirect |
| 2. C22×#14579102 | C2 | semidirect |
| 3. C2×#19098947 | C2 | semidirect |
| 4. #23765664 | C2 | direct (N × H) |
| 5. C2×#19098339 | C2 | semidirect |
| 6. C2×#493×C79 | C2 | semidirect |
| 12. C2×#14579105 | C22 | semidirect |
| 14. C2×#14579102 | C22 | semidirect |
| 17. #19098947 | C22 | semidirect |
| 18. #19098339 | C22 | semidirect |
| 23. #493×C79 | C22 | semidirect |
| 40. C2×C79⋊C16 | D4 | semidirect |
| 73. C79⋊C16 | C2×D4 | semidirect |
| 138. C2×C79 | #2250 | semidirect |
| 145. C2×#493 | D79 | semidirect |
| 148. C79 | C2×#2250 | semidirect |
| 164. #493 | C2×D79 | semidirect |
| 280. C2 | #23765664 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579105 | 2 |
| C22×#14579102 | 2 |
| C2×#19098947 | 2 |
| #23765664 | 2 |
| C2×#19098339 | 2 |
| C2×#493×C79 | 2 |
| C2×#2250 | 79 |