Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
724 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 724 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 |
|---|---|---|
| 2. C2×#19098355 | C2 | semidirect |
| 3. C4×#14579076 | C2 | semidirect |
| 4. C79×#1799 | C2 | semidirect |
| 5. C2×#14579158 | C4 | semidirect |
| 12. #19098464 | C4 | semidirect |
| 13. C4×C4⋊Dic79 | C4 | semidirect |
| 39. #14579076 | D4 | semidirect |
| 190. C4×C79 | #353 | semidirect |
| 205. #1799 | D79 | semidirect |
| 207. C79 | #13223 | semidirect |
| 395. C4 | #19098355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23768346 | 2 |
| C2×#19098355 | 2 |
| C4×#14579076 | 2 |
| C79×#1799 | 2 |
| #13223 | 79 |