Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
512 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 127 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. #23774043 | C2 | semidirect |
| 2. #23765560 | C2 | semidirect |
| 3. #23765555 | C2 | semidirect |
| 4. #23765501 | C2 | semidirect |
| 5. #23765486 | C2 | semidirect |
| 6. #23765434 | C2 | semidirect |
| 7. #23765433 | C2 | semidirect |
| 8. #23765158 | C2 | semidirect |
| 9. C79×#2215 | C2 | semidirect |
| 157. #2215 | D79 | semidirect |
| 161. C79 | #33825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774043 | 2 |
| #23765560 | 2 |
| #23765555 | 2 |
| #23765501 | 2 |
| #23765486 | 2 |
| #23765434 | 2 |
| #23765433 | 2 |
| #23765158 | 2 |
| C79×#2215 | 2 |
| #33825 | 79 |