Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
786 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 187 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. C22×#14579100 | C2 | semidirect |
| 3. C2×#19098800 | C2 | semidirect |
| 4. #23765504 | C2 | direct (N × H) |
| 5. C2×#19098363 | C2 | semidirect |
| 6. C2×#367×C79 | C2 | semidirect |
| 11. C2×D1264 | C22 | semidirect |
| 13. C2×#14579100 | C22 | semidirect |
| 16. #19098800 | C22 | semidirect |
| 18. #19098363 | C22 | semidirect |
| 21. #367×C79 | C22 | semidirect |
| 44. C2×C16×C79 | D4 | semidirect |
| 79. C16×C79 | C2×D4 | semidirect |
| 123. C2×C79 | #2218 | semidirect |
| 132. C2×#367 | D79 | semidirect |
| 134. C79 | C2×#2218 | semidirect |
| 148. #367 | C2×D79 | semidirect |
| 171. C2×C16 | D316 | semidirect |
| 207. C16 | C2×D316 | semidirect |
| 252. C2 | #23765504 | 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 |
| C22×#14579100 | 2 |
| C2×#19098800 | 2 |
| #23765504 | 2 |
| C2×#19098363 | 2 |
| C2×#367×C79 | 2 |
| C2×#2218 | 79 |