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. #23763681 | C2 | semidirect |
| 5. #23761518 | C2 | semidirect |
| 6. #23761517 | C2 | semidirect |
| 7. C79×#1867 | C2 | semidirect |
| 20. #19098355 | C4 | semidirect |
| 57. #14579076 | C2×C4 | semidirect |
| 72. #99×C79 | C2×C4 | semidirect |
| 79. C2×D316 | C4⋊C4 | semidirect |
| 113. C4×Dic79 | C4⋊C4 | semidirect |
| 262. #1867 | 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 |
| #23763798 | 2 |
| #23763681 | 2 |
| #23761518 | 2 |
| #23761517 | 2 |
| C79×#1867 | 2 |
| #12964 | 79 |