Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
636 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 143 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. #23776550 | C2 | semidirect |
| 2. #23775205 | C2 | semidirect |
| 3. #23765653 | C2 | semidirect |
| 4. #23765526 | C2 | semidirect |
| 5. #23765481 | C2 | semidirect |
| 6. #23765379 | C2 | semidirect |
| 7. #23765238 | C2 | semidirect |
| 8. C79×#2178 | C2 | semidirect |
| 145. #2178 | D79 | semidirect |
| 147. C79 | #33860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776550 | 2 |
| #23775205 | 2 |
| #23765653 | 2 |
| #23765526 | 2 |
| #23765481 | 2 |
| #23765379 | 2 |
| #23765238 | 2 |
| C79×#2178 | 2 |
| #33860 | 79 |