Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
500 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23773431 | C2 | semidirect |
| 3. #23762034 | C2 | semidirect |
| 4. #23761869 | C2 | semidirect |
| 5. #23761744 | C2 | semidirect |
| 6. #23761261 | C2 | semidirect |
| 7. C79×#3112 | C2 | semidirect |
| 198. #3112 | D79 | semidirect |
| 204. C79 | #10040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774395 | 2 |
| #23773431 | 2 |
| #23762034 | 2 |
| #23761869 | 2 |
| #23761744 | 2 |
| #23761261 | 2 |
| C79×#3112 | 2 |
| #10040 | 79 |