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 |
|---|---|---|
| 1. #23775831 | C2 | semidirect |
| 2. #23765624 | C2 | semidirect |
| 3. #23765441 | C2 | semidirect |
| 5. #23761454 | C2 | semidirect |
| 6. #23761365 | C2 | semidirect |
| 7. C79×D4⋊C16 | C2 | semidirect |
| 141. D4⋊C16 | D79 | semidirect |
| 142. C79 | #12341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775831 | 2 |
| #23765624 | 2 |
| #23765441 | 2 |
| #23762755 | 2 |
| #23761454 | 2 |
| #23761365 | 2 |
| C79×D4⋊C16 | 2 |
| #12341 | 79 |