Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
2502 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 667 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×#14579155 | C2 | semidirect |
| 2. #23771474 | C2 | direct (N × H) |
| 3. C2×#19098493 | C2 | semidirect |
| 4. C2×#19098485 | C2 | semidirect |
| 6. C2×#384×C79 | C2 | semidirect |
| 9. C2×#14579155 | C22 | semidirect |
| 14. #19098493 | C22 | semidirect |
| 15. #19098485 | C22 | semidirect |
| 22. #384×C79 | C22 | semidirect |
| 45. C2×C42×C79 | D4 | semidirect |
| 73. C42×C79 | C2×D4 | semidirect |
| 113. C2×C79 | #2823 | semidirect |
| 123. C2×#384 | D79 | semidirect |
| 124. C79 | C2×#2823 | semidirect |
| 138. #384 | C2×D79 | semidirect |
| 161. C2×C42 | D316 | semidirect |
| 191. C42 | C2×D316 | semidirect |
| 231. C2 | #23771474 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579155 | 2 |
| #23771474 | 2 |
| C2×#19098493 | 2 |
| C2×#19098485 | 2 |
| C2×#19098480 | 2 |
| C2×#384×C79 | 2 |
| C2×#2823 | 79 |