Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
190 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #23761605 | C2 | direct (N × H) |
| 6. #19098397 | C4 | semidirect |
| 8. C2×C79⋊C32 | C4 | semidirect |
| 18. C79⋊C32 | C2×C4 | semidirect |
| 72. C2×C79 | #1426 | semidirect |
| 78. C79 | C2×#1426 | semidirect |
| 145. C2 | #23761605 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098397 | 2 |
| C2×#19098393 | 2 |
| #23761605 | 2 |
| C2×#367×C79 | 2 |
| C2×#1426 | 79 |