Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
372 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23765019 | C2 | semidirect |
| 3. #23761351 | C2 | semidirect |
| 4. #23761337 | C2 | semidirect |
| 5. C79×#1327 | C2 | semidirect |
| 140. #1327 | D79 | semidirect |
| 142. C79 | #11485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772111 | 2 |
| #23765019 | 2 |
| #23761351 | 2 |
| #23761337 | 2 |
| C79×#1327 | 2 |
| #11485 | 79 |