Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
384 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 97 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. C4×#14579094 | C2 | semidirect |
| 3. #23762161 | C2 | semidirect |
| 6. #23761257 | C2 | semidirect |
| 7. C79×#1285 | C2 | semidirect |
| 9. #19098690 | C4 | semidirect |
| 10. #19098687 | C4 | semidirect |
| 11. #19098640 | C4 | semidirect |
| 13. #19098628 | C4 | semidirect |
| 185. #1285 | D79 | semidirect |
| 186. C79 | #8697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772369 | 2 |
| C4×#14579094 | 2 |
| #23762161 | 2 |
| #23761926 | 2 |
| #23761923 | 2 |
| #23761257 | 2 |
| C79×#1285 | 2 |
| #8697 | 79 |