Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 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 |
|---|---|---|
| 1. #23776502 | C2 | semidirect |
| 3. #23765137 | C2 | semidirect |
| 4. #23765135 | C2 | semidirect |
| 5. #23763443 | C2 | semidirect |
| 6. #23761507 | C2 | semidirect |
| 7. C79×#1386 | C2 | semidirect |
| 15. #19098822 | C4 | semidirect |
| 16. #19098817 | C4 | semidirect |
| 50. #14579101 | D4 | semidirect |
| 63. M32×C79 | D4 | semidirect |
| 188. #1386 | D79 | semidirect |
| 189. C79 | #13077 | semidirect |
| 238. M32 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776502 | 2 |
| #23773063 | 2 |
| #23765137 | 2 |
| #23765135 | 2 |
| #23763443 | 2 |
| #23761507 | 2 |
| C79×#1386 | 2 |
| #13077 | 79 |