Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
672 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #23763683 | C2 | semidirect |
| 5. #23763680 | C2 | semidirect |
| 6. #23761519 | C2 | semidirect |
| 7. C79×#1390 | C2 | semidirect |
| 21. #19098355 | C4 | semidirect |
| 60. #14579076 | C2×C4 | semidirect |
| 73. #99×C79 | C2×C4 | semidirect |
| 79. C2×D316 | C4⋊C4 | semidirect |
| 121. C4×Dic79 | C4⋊C4 | semidirect |
| 264. #1390 | D79 | semidirect |
| 265. C79 | #12964 | semidirect |
| 328. #99 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766463 | 2 |
| C2×#19098355 | 2 |
| #23763796 | 2 |
| #23763683 | 2 |
| #23763680 | 2 |
| #23761519 | 2 |
| C79×#1390 | 2 |
| #12964 | 79 |