Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
296 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. #23762767 | C2 | semidirect |
| 4. #23761458 | C2 | semidirect |
| 5. #23761380 | C2 | semidirect |
| 7. C79×#2241 | C2 | semidirect |
| 127. #2241 | D79 | semidirect |
| 133. C79 | #12359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776269 | 2 |
| #23765442 | 2 |
| #23762767 | 2 |
| #23761458 | 2 |
| #23761380 | 2 |
| #23761362 | 2 |
| C79×#2241 | 2 |
| #12359 | 79 |