Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
334 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×#19098398 | C2 | semidirect |
| 2. #23765486 | C2 | semidirect |
| 3. #23761578 | C2 | semidirect |
| 4. C22⋊(C79⋊C32) | C2 | semidirect |
| 5. C22×D16×C79 | C2 | semidirect |
| 6. C2×D1264 | C22 | semidirect |
| 9. C2×C79⋊C32 | C22 | semidirect |
| 10. #19098389 | C22 | semidirect |
| 31. D16×C79 | D4 | semidirect |
| 82. C22×C79 | D32 | semidirect |
| 98. C22×D16 | D79 | semidirect |
| 103. C79 | #13661 | semidirect |
| 126. D16 | C22⋊D79 | semidirect |
| 183. C22 | #19098398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098398 | 2 |
| #23765486 | 2 |
| #23761578 | 2 |
| C22⋊(C79⋊C32) | 2 |
| C22×D16×C79 | 2 |
| #13661 | 79 |