Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
466 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 107 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×#19098375 | C2 | semidirect |
| 3. #23765135 | C2 | semidirect |
| 4. #23765127 | C2 | semidirect |
| 5. #23765115 | C2 | semidirect |
| 6. #23765005 | C2 | semidirect |
| 7. C79×#1833 | C2 | semidirect |
| 15. #19098947 | C4 | semidirect |
| 16. #19098940 | C4 | semidirect |
| 53. #14579101 | D4 | semidirect |
| 55. C2×C79⋊C16 | D4 | semidirect |
| 181. #1833 | D79 | semidirect |
| 182. C79 | #13215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773886 | 2 |
| C2×#19098375 | 2 |
| #23765135 | 2 |
| #23765127 | 2 |
| #23765115 | 2 |
| #23765005 | 2 |
| C79×#1833 | 2 |
| #13215 | 79 |