Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
516 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 516 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. #23771988 | C2 | semidirect |
| 3. #23765137 | C2 | semidirect |
| 4. #23765135 | C2 | semidirect |
| 5. C2×#19098344 | C2 | semidirect |
| 6. #23761501 | C2 | semidirect |
| 7. C79×#1384 | C2 | semidirect |
| 13. #19098822 | C4 | semidirect |
| 14. #19098817 | C4 | semidirect |
| 33. C2×Dic316 | C2×C4 | semidirect |
| 35. C2×D632 | C2×C4 | semidirect |
| 60. #14579093 | D4 | semidirect |
| 72. #106×C79 | C2×C4 | semidirect |
| 73. #106×C79 | D4 | semidirect |
| 199. #1384 | D79 | semidirect |
| 200. C79 | #13008 | semidirect |
| 263. #106 | C4×D79 | semidirect |
| 264. #106 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773010 | 2 |
| #23771988 | 2 |
| #23765137 | 2 |
| #23765135 | 2 |
| C2×#19098344 | 2 |
| #23761501 | 2 |
| C79×#1384 | 2 |
| #13008 | 79 |