Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
680 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 171 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. #23772268 | C2 | semidirect |
| 4. #23765464 | C2 | semidirect |
| 5. #23765448 | C2 | semidirect |
| 6. #23765158 | C2 | semidirect |
| 7. #23765120 | C2 | semidirect |
| 9. C22×Q32×C79 | C2 | semidirect |
| 173. C22×Q32 | D79 | semidirect |
| 181. C79 | #33588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099004 | 2 |
| #23773889 | 2 |
| #23772268 | 2 |
| #23765464 | 2 |
| #23765448 | 2 |
| #23765158 | 2 |
| #23765120 | 2 |
| #23765108 | 2 |
| C22×Q32×C79 | 2 |
| #33588 | 79 |