Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#19098998 | C2 | semidirect |
| 2. C2×#19098833 | C2 | semidirect |
| 3. C2×#19098370 | C2 | semidirect |
| 4. C2×#19098363 | C2 | semidirect |
| 5. C2×#19098347 | C2 | semidirect |
| 6. #23761508 | C2 | semidirect |
| 7. C79×#3061 | C2 | semidirect |
| 40. C2×D632 | D4 | semidirect |
| 46. #14579101 | D4 | semidirect |
| 52. #14579097 | D4 | semidirect |
| 221. #3061 | D79 | semidirect |
| 226. C79 | #13307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098998 | 2 |
| C2×#19098833 | 2 |
| C2×#19098370 | 2 |
| C2×#19098363 | 2 |
| C2×#19098347 | 2 |
| #23761508 | 2 |
| C79×#3061 | 2 |
| #13307 | 79 |