Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23772284 | C2 | semidirect |
| 3. C2×#19098374 | C2 | semidirect |
| 4. #23764296 | C2 | semidirect |
| 5. #23761505 | C2 | semidirect |
| 6. #23761485 | C2 | semidirect |
| 7. C79×#2145 | C2 | semidirect |
| 11. #19099003 | C4 | semidirect |
| 13. #19098998 | C4 | semidirect |
| 34. C2×Dic316 | C2×C4 | semidirect |
| 36. C2×D632 | C2×C4 | semidirect |
| 50. #14579101 | C2×C4 | semidirect |
| 192. #2145 | D79 | semidirect |
| 197. C79 | #13030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776534 | 2 |
| #23772284 | 2 |
| C2×#19098374 | 2 |
| #23764296 | 2 |
| #23761505 | 2 |
| #23761485 | 2 |
| C79×#2145 | 2 |
| #13030 | 79 |