Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
2398 conjugacy classes of subgroups; only the 1067 normal subgroups are shown.
This group has 2398 conjugacy classes of subgroups — too many to draw. Only its 1067 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×#19098961 | C2 | direct (N × H) |
| 10. #19098961 | C22 | direct (N × H) |
| 26. C22×C8×C79 | Q8 | semidirect |
| 44. C2×C8×C79 | C2×Q8 | semidirect |
| 60. C8×C79 | C22×Q8 | semidirect |
| 61. C22×C79 | #498 | semidirect |
| 70. C2×C79 | C2×#498 | semidirect |
| 77. C79 | C22×#498 | semidirect |
| 93. C22×C8 | Dic158 | semidirect |
| 114. C2×C8 | C2×Dic158 | semidirect |
| 133. C8 | C22×Dic158 | semidirect |
| 134. C22 | #19098961 | direct (N × H) |
| 142. C2 | C2×#19098961 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579161 | 2 |
| C2×#19098961 | 2 |
| C22×#14579093 | 2 |
| C22×C4×C8×C79 | 2 |
| C22×#498 | 79 |