Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
286 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 71 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. #23765212 | C2 | semidirect |
| 3. #23761393 | C2 | semidirect |
| 5. #23761387 | C2 | semidirect |
| 7. C79×#1841 | C2 | semidirect |
| 9. #19098965 | C4 | semidirect |
| 10. #19098947 | C4 | semidirect |
| 15. #19098676 | C4 | semidirect |
| 16. #19098671 | C4 | semidirect |
| 142. #1841 | D79 | semidirect |
| 147. C79 | #11836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774129 | 2 |
| #23765212 | 2 |
| #23761393 | 2 |
| #23761390 | 2 |
| #23761387 | 2 |
| #23761384 | 2 |
| C79×#1841 | 2 |
| #11836 | 79 |