Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
402 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23765194 | C2 | semidirect |
| 3. C2×#19098377 | C2 | semidirect |
| 4. C2×#19098375 | C2 | semidirect |
| 5. #23765027 | C2 | semidirect |
| 6. #23763447 | C2 | semidirect |
| 7. C79×#1388 | C2 | semidirect |
| 170. #1388 | D79 | semidirect |
| 171. C79 | #13389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098834 | 2 |
| #23765194 | 2 |
| C2×#19098377 | 2 |
| C2×#19098375 | 2 |
| #23765027 | 2 |
| #23763447 | 2 |
| C79×#1388 | 2 |
| #13389 | 79 |