Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
464 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. #23765009 | C2 | semidirect |
| 3. #23763424 | C2 | semidirect |
| 4. #23761410 | C2 | semidirect |
| 5. #23761409 | C2 | semidirect |
| 6. #23761408 | C2 | semidirect |
| 7. C79×#1347 | C2 | semidirect |
| 8. C2×D8×D79 | C4 | semidirect |
| 12. #19098800 | C4 | semidirect |
| 16. #19098796 | C4 | semidirect |
| 17. #107×D79 | C4 | semidirect |
| 21. C22⋊(C79⋊C16) | C22 | semidirect |
| 23. #19098326 | C22 | semidirect |
| 25. C22⋊C16×C79 | C22 | semidirect |
| 26. #340×C79 | C22 | semidirect |
| 209. #1347 | D79 | semidirect |
| 210. C79 | #11888 | semidirect |
| 227. C22⋊C16 | C2×D79 | semidirect |
| 229. #340 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #466×D79 | 2 |
| #23765009 | 2 |
| #23763424 | 2 |
| #23761410 | 2 |
| #23761409 | 2 |
| #23761408 | 2 |
| C79×#1347 | 2 |
| #11888 | 79 |