Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
320 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23765200 | C2 | semidirect |
| 3. #23765196 | C2 | semidirect |
| 4. #23761340 | C2 | semidirect |
| 7. C79×#1322 | C2 | semidirect |
| 163. #1322 | D79 | semidirect |
| 166. C79 | #11461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098623 | 2 |
| #23765200 | 2 |
| #23765196 | 2 |
| #23761340 | 2 |
| #23761323 | 2 |
| C79×#1322 | 2 |
| #11461 | 79 |