Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
386 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 75 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. #23763575 | C2 | semidirect |
| 3. #23762123 | C2 | semidirect |
| 4. #23762122 | C2 | semidirect |
| 5. #23762010 | C2 | semidirect |
| 6. #23761310 | C2 | semidirect |
| 7. C79×#1530 | C2 | semidirect |
| 168. #1530 | D79 | semidirect |
| 170. C79 | #10524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774778 | 2 |
| #23763575 | 2 |
| #23762123 | 2 |
| #23762122 | 2 |
| #23762010 | 2 |
| #23761310 | 2 |
| C79×#1530 | 2 |
| #10524 | 79 |