Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
3798 conjugacy classes of subgroups; only the 1179 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 1179 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. #23766577 | C2 | direct (N × H) |
| 2. C2×#19098443 | C2 | semidirect |
| 3. C2×#19098431 | C2 | semidirect |
| 7. #19098443 | C22 | semidirect |
| 8. #19098431 | C22 | semidirect |
| 11. C2×#127×C79 | C4 | semidirect |
| 23. C22×D4×C79 | C2×C4 | semidirect |
| 26. #127×C79 | C2×C4 | semidirect |
| 27. C2×C42×C79 | C2×C4 | semidirect |
| 42. C2×D4×C79 | C22×C4 | semidirect |
| 46. C42×C79 | C22×C4 | semidirect |
| 75. C2×C79 | #2380 | semidirect |
| 82. C79 | C2×#2380 | semidirect |
| 85. C2×#127 | Dic79 | semidirect |
| 95. C22×D4 | C2×Dic79 | semidirect |
| 101. #127 | C2×Dic79 | semidirect |
| 104. C2×C42 | C2×Dic79 | semidirect |
| 115. C2×D4 | C22×Dic79 | semidirect |
| 124. C42 | C22×Dic79 | semidirect |
| 152. C2 | #23766577 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766577 | 2 |
| C2×#19098443 | 2 |
| C2×#19098431 | 2 |
| C22×#127×C79 | 2 |
| C2×#2380 | 79 |