Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
3798 conjugacy classes of subgroups; only the 923 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 923 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. #23766576 | C2 | direct (N × H) |
| 3. C2×#19098441 | C2 | semidirect |
| 4. C2×#19098431 | C2 | semidirect |
| 5. C2×#383×C79 | C2 | semidirect |
| 8. C2×#14579158 | C4 | semidirect |
| 11. #19098441 | C22 | semidirect |
| 12. #19098431 | C22 | semidirect |
| 15. #383×C79 | C22 | semidirect |
| 20. C22×D316 | C2×C4 | semidirect |
| 25. #14579158 | C2×C4 | semidirect |
| 31. C2×C42×C79 | C2×C4 | semidirect |
| 41. C2×D316 | C22×C4 | semidirect |
| 53. C42×C79 | C22×C4 | semidirect |
| 84. C2×C79 | #2380 | semidirect |
| 92. C2×#383 | D79 | semidirect |
| 93. C79 | C2×#2380 | semidirect |
| 102. #383 | C2×D79 | semidirect |
| 118. C2×C42 | C4×D79 | semidirect |
| 141. C42 | C2×C4×D79 | semidirect |
| 172. C2 | #23766576 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579158 | 2 |
| #23766576 | 2 |
| C2×#19098441 | 2 |
| C2×#19098431 | 2 |
| C2×#383×C79 | 2 |
| C2×#2380 | 79 |