Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 290 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 |
|---|---|---|
| 2. #23765673 | C2 | semidirect |
| 3. #23765544 | C2 | semidirect |
| 4. #23761459 | C2 | semidirect |
| 5. #23761360 | C2 | semidirect |
| 6. D4⋊(C79⋊C16) | C2 | semidirect |
| 7. C79×#1675 | C2 | semidirect |
| 131. #1675 | D79 | semidirect |
| 135. C79 | #12399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775823 | 2 |
| #23765673 | 2 |
| #23765544 | 2 |
| #23761459 | 2 |
| #23761360 | 2 |
| D4⋊(C79⋊C16) | 2 |
| C79×#1675 | 2 |
| #12399 | 79 |