Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
798 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 227 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 |
|---|---|---|
| 2. C2×#19098645 | C2 | semidirect |
| 3. #23765275 | C2 | direct (N × H) |
| 4. C2×#19098363 | C2 | semidirect |
| 5. C2×#19098338 | C2 | semidirect |
| 6. C2×#367×C79 | C2 | semidirect |
| 9. C2×D1264 | C4 | semidirect |
| 13. #19098645 | C22 | semidirect |
| 16. #19098363 | C22 | semidirect |
| 17. #19098338 | C22 | semidirect |
| 20. #367×C79 | C22 | semidirect |
| 25. C2×D632 | C2×C4 | semidirect |
| 32. D1264 | C2×C4 | semidirect |
| 40. C2×C16×C79 | C2×C4 | semidirect |
| 54. D632 | C22×C4 | semidirect |
| 69. C16×C79 | C22×C4 | semidirect |
| 104. C2×C79 | #2177 | semidirect |
| 111. C2×#367 | D79 | semidirect |
| 114. C79 | C2×#2177 | semidirect |
| 126. #367 | C2×D79 | semidirect |
| 145. C2×C16 | C4×D79 | semidirect |
| 177. C16 | C2×C4×D79 | semidirect |
| 212. C2 | #23765275 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1264 | 2 |
| C2×#19098645 | 2 |
| #23765275 | 2 |
| C2×#19098363 | 2 |
| C2×#19098338 | 2 |
| C2×#367×C79 | 2 |
| C2×#2177 | 79 |