Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
334 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 67 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. C22×D1264 | C2 | semidirect |
| 2. C2×D2528 | C2 | semidirect |
| 3. #23765486 | C2 | semidirect |
| 4. #23761579 | C2 | semidirect |
| 5. C79×C22⋊C32 | C2 | semidirect |
| 10. C2×D1264 | C22 | semidirect |
| 13. #19098389 | C22 | semidirect |
| 16. C2×C32×C79 | C22 | semidirect |
| 27. D1264 | D4 | semidirect |
| 78. C22×C79 | D32 | semidirect |
| 102. C22⋊C32 | D79 | semidirect |
| 103. C79 | #13661 | semidirect |
| 112. C2×C32 | C2×D79 | semidirect |
| 183. C22 | D2528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1264 | 2 |
| C2×D2528 | 2 |
| #23765486 | 2 |
| #23761579 | 2 |
| C79×C22⋊C32 | 2 |
| #13661 | 79 |