Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
806 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 195 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×C16×D79 | C2 | semidirect |
| 3. C2×#19098800 | C2 | semidirect |
| 4. #23765487 | C2 | direct (N × H) |
| 5. C2×#19098363 | C2 | semidirect |
| 6. C2×#366×C79 | C2 | semidirect |
| 11. C2×D1264 | C22 | semidirect |
| 14. C2×C16×D79 | C22 | semidirect |
| 16. #19098800 | C22 | semidirect |
| 18. #19098363 | C22 | semidirect |
| 21. #366×C79 | C22 | semidirect |
| 44. C2×C16×C79 | D4 | semidirect |
| 79. C16×C79 | C2×D4 | semidirect |
| 87. C22×D79 | D16 | semidirect |
| 119. C2×D79 | C2×D16 | semidirect |
| 126. C2×C79 | #2215 | semidirect |
| 136. C2×#366 | D79 | semidirect |
| 138. C79 | C2×#2215 | semidirect |
| 152. #366 | C2×D79 | semidirect |
| 175. C2×C16 | D316 | semidirect |
| 211. C16 | C2×D316 | semidirect |
| 259. C2 | #23765487 | 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×C16×D79 | 2 |
| C2×#19098800 | 2 |
| #23765487 | 2 |
| C2×#19098363 | 2 |
| C2×#366×C79 | 2 |
| C2×#2215 | 79 |