Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
470 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 155 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×#19098995 | C2 | semidirect |
| 2. #23765707 | C2 | direct (N × H) |
| 3. C2×#19098403 | C2 | semidirect |
| 4. C2×#19098401 | C2 | semidirect |
| 5. C2×#19098400 | C2 | semidirect |
| 6. C2×#19098398 | C2 | semidirect |
| 7. C22×C79⋊C32 | C2 | semidirect |
| 8. C2×#508×C79 | C2 | semidirect |
| 11. #19098995 | C22 | semidirect |
| 15. #19098403 | C22 | semidirect |
| 16. #19098401 | C22 | semidirect |
| 17. #19098400 | C22 | semidirect |
| 18. #19098398 | C22 | semidirect |
| 21. C2×C79⋊C32 | C22 | semidirect |
| 24. #508×C79 | C22 | semidirect |
| 127. C2×C79 | #2262 | semidirect |
| 131. C2×#508 | D79 | semidirect |
| 138. C79 | C2×#2262 | semidirect |
| 144. #508 | C2×D79 | semidirect |
| 257. C2 | #23765707 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098995 | 2 |
| #23765707 | 2 |
| C2×#19098403 | 2 |
| C2×#19098401 | 2 |
| C2×#19098400 | 2 |
| C2×#19098398 | 2 |
| C22×C79⋊C32 | 2 |
| C2×#508×C79 | 2 |
| C2×#2262 | 79 |