Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1022 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 219 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×#14579102 | C2 | semidirect |
| 3. C2×#19098938 | C2 | semidirect |
| 4. #23765648 | C2 | direct (N × H) |
| 5. C2×C16×Dic79 | C2 | semidirect |
| 6. C22×D16×C79 | C2 | semidirect |
| 11. C2×D1264 | C22 | semidirect |
| 13. C2×#14579102 | C22 | semidirect |
| 16. #19098938 | C22 | semidirect |
| 18. C16×Dic79 | C22 | semidirect |
| 21. C2×D16×C79 | C22 | semidirect |
| 37. C2×C79⋊C16 | D4 | semidirect |
| 48. C2×C16×C79 | D4 | semidirect |
| 66. C79⋊C16 | C2×D4 | semidirect |
| 80. C16×C79 | C2×D4 | semidirect |
| 96. C2×Dic79 | D16 | semidirect |
| 117. Dic79 | C2×D16 | semidirect |
| 120. C2×C79 | #2246 | semidirect |
| 126. C22×D16 | D79 | semidirect |
| 130. C79 | C2×#2246 | semidirect |
| 140. C2×D16 | C2×D79 | semidirect |
| 170. C2×C16 | C22⋊D79 | semidirect |
| 204. C16 | C2×C22⋊D79 | semidirect |
| 244. C2 | #23765648 | 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×#14579102 | 2 |
| C2×#19098938 | 2 |
| #23765648 | 2 |
| C2×C16×Dic79 | 2 |
| C22×D16×C79 | 2 |
| C2×#2246 | 79 |