Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1134 conjugacy classes of subgroups; only the 555 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 555 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. #23763543 | C2 | direct (N × H) |
| 18. C2×C42×C79 | C8 | semidirect |
| 40. C42×C79 | C2×C8 | semidirect |
| 68. C2×C79 | #1839 | semidirect |
| 75. C79 | C2×#1839 | semidirect |
| 90. C2×C42 | C79⋊C8 | semidirect |
| 112. C42 | C2×C79⋊C8 | semidirect |
| 139. C2 | #23763543 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763543 | 2 |
| C2×#19098318 | 2 |
| C2×C43×C79 | 2 |
| C2×#1839 | 79 |