Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 306 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. #23765543 | C2 | semidirect |
| 4. #23762794 | C2 | semidirect |
| 6. #23761365 | C2 | semidirect |
| 7. C79×Q8⋊C16 | C2 | semidirect |
| 134. Q8⋊C16 | D79 | semidirect |
| 136. C79 | #12381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776413 | 2 |
| #23765624 | 2 |
| #23765543 | 2 |
| #23762794 | 2 |
| #23761447 | 2 |
| #23761365 | 2 |
| C79×Q8⋊C16 | 2 |
| #12381 | 79 |