Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
918 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 179 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×#19098997 | C2 | semidirect |
| 2. #23773827 | C2 | semidirect |
| 3. #493×D79 | C2 | semidirect |
| 4. #23765663 | C2 | semidirect |
| 5. #23765656 | C2 | semidirect |
| 6. #23765655 | C2 | semidirect |
| 7. #23765649 | C2 | semidirect |
| 8. C4×#14579100 | C2 | semidirect |
| 9. C79×#2246 | C2 | semidirect |
| 17. C2×#14579106 | C22 | semidirect |
| 18. C2×#14579105 | C22 | semidirect |
| 19. C2×#14579102 | C22 | semidirect |
| 22. #19098946 | C22 | semidirect |
| 23. #19098943 | C22 | semidirect |
| 30. #19098338 | C22 | semidirect |
| 31. C4×C79⋊C16 | C22 | semidirect |
| 32. C2×D16×C79 | C22 | semidirect |
| 34. #493×C79 | C22 | semidirect |
| 35. C4×C16×C79 | C22 | semidirect |
| 64. #14579100 | D4 | semidirect |
| 109. C79⋊C16 | C2×D4 | semidirect |
| 121. C16×C79 | C2×D4 | semidirect |
| 165. C4×C79 | #509 | semidirect |
| 185. #2246 | D79 | semidirect |
| 187. C79 | #33717 | semidirect |
| 198. C2×D16 | C2×D79 | semidirect |
| 208. #493 | C2×D79 | semidirect |
| 213. C4×C16 | C2×D79 | semidirect |
| 299. C16 | D4×D79 | semidirect |
| 346. C4 | #19098997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098997 | 2 |
| #23773827 | 2 |
| #493×D79 | 2 |
| #23765663 | 2 |
| #23765656 | 2 |
| #23765655 | 2 |
| #23765649 | 2 |
| C4×#14579100 | 2 |
| C79×#2246 | 2 |
| #33717 | 79 |