Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
820 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23763869 | C2 | semidirect |
| 3. #23763861 | C2 | semidirect |
| 4. #23763695 | C2 | semidirect |
| 5. #23761759 | C2 | semidirect |
| 6. #23761736 | C2 | semidirect |
| 7. C79×#1472 | C2 | semidirect |
| 312. #1472 | D79 | semidirect |
| 315. C79 | #8538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777241 | 2 |
| #23763869 | 2 |
| #23763861 | 2 |
| #23763695 | 2 |
| #23761759 | 2 |
| #23761736 | 2 |
| C79×#1472 | 2 |
| #8538 | 79 |