Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
564 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23774138 | C2 | semidirect |
| 2. #23772311 | C2 | semidirect |
| 3. #23765615 | C2 | semidirect |
| 4. #23765572 | C2 | semidirect |
| 5. #23765477 | C2 | semidirect |
| 6. #23765348 | C2 | semidirect |
| 7. #23765300 | C2 | semidirect |
| 8. C79×#2165 | C2 | semidirect |
| 13. #19098961 | C22 | semidirect |
| 14. #19098940 | C22 | semidirect |
| 23. #19098676 | C22 | semidirect |
| 26. #19098386 | C22 | semidirect |
| 27. #19098377 | C22 | semidirect |
| 30. #364×C79 | C22 | semidirect |
| 32. #347×C79 | C22 | semidirect |
| 87. Dic316 | #41 | semidirect |
| 93. D632 | #41 | semidirect |
| 177. #2165 | D79 | semidirect |
| 178. C79 | #33688 | semidirect |
| 198. #364 | C2×D79 | semidirect |
| 202. #347 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774138 | 2 |
| #23772311 | 2 |
| #23765615 | 2 |
| #23765572 | 2 |
| #23765477 | 2 |
| #23765348 | 2 |
| #23765300 | 2 |
| C79×#2165 | 2 |
| #33688 | 79 |