Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
322 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 73 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. #23765628 | C2 | semidirect |
| 4. #23762770 | C2 | semidirect |
| 5. #23761454 | C2 | semidirect |
| 7. C79×Q8⋊C16 | C2 | semidirect |
| 87. Q8×C79 | SD32 | semidirect |
| 135. Q8⋊C16 | D79 | semidirect |
| 137. C79 | #12356 | semidirect |
| 222. Q8 | #14579106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D632 | 2 |
| #23765628 | 2 |
| #23765446 | 2 |
| #23762770 | 2 |
| #23761454 | 2 |
| #23761362 | 2 |
| C79×Q8⋊C16 | 2 |
| #12356 | 79 |