Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
568 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. #23776534 | C2 | semidirect |
| 2. C2×#19099001 | C2 | semidirect |
| 3. #23773887 | C2 | semidirect |
| 4. #23765115 | C2 | semidirect |
| 5. #23764296 | C2 | semidirect |
| 6. #23761487 | C2 | semidirect |
| 7. C79×#2145 | C2 | semidirect |
| 41. C2×Dic316 | D4 | semidirect |
| 50. C2×D632 | D4 | semidirect |
| 66. C2×C79⋊C16 | D4 | semidirect |
| 82. M32×C79 | D4 | semidirect |
| 221. #2145 | D79 | semidirect |
| 225. C79 | #13334 | semidirect |
| 295. M32 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776534 | 2 |
| C2×#19099001 | 2 |
| #23773887 | 2 |
| #23765115 | 2 |
| #23764296 | 2 |
| #23761487 | 2 |
| C79×#2145 | 2 |
| #13334 | 79 |