Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
536 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#19099004 | C2 | semidirect |
| 3. #23765136 | C2 | semidirect |
| 4. #23765120 | C2 | semidirect |
| 5. #23764298 | C2 | semidirect |
| 6. #23761486 | C2 | semidirect |
| 7. C79×#3156 | C2 | semidirect |
| 214. #3156 | D79 | semidirect |
| 219. C79 | #13335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776534 | 2 |
| C2×#19099004 | 2 |
| #23765136 | 2 |
| #23765120 | 2 |
| #23764298 | 2 |
| #23761486 | 2 |
| C79×#3156 | 2 |
| #13335 | 79 |