Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
588 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 3. #23763388 | C2 | semidirect |
| 4. #23761524 | C2 | semidirect |
| 5. C79×#1799 | C2 | semidirect |
| 7. C2×C4×D316 | C4 | semidirect |
| 10. #19098464 | C4 | semidirect |
| 15. #19098428 | C4 | semidirect |
| 17. #19098409 | C4 | semidirect |
| 69. C2×D316 | C4⋊C4 | semidirect |
| 97. C4×Dic79 | C4⋊C4 | semidirect |
| 241. #1799 | D79 | semidirect |
| 243. C79 | #12799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766122 | 2 |
| C2×#19098355 | 2 |
| #23763388 | 2 |
| #23761524 | 2 |
| C79×#1799 | 2 |
| #12799 | 79 |