Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
378 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23765158 | C2 | semidirect |
| 5. #23763525 | C2 | semidirect |
| 6. #23761514 | C2 | semidirect |
| 7. C79×#1381 | C2 | semidirect |
| 11. #19098684 | C4 | semidirect |
| 149. #1381 | D79 | semidirect |
| 150. C79 | #12829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772316 | 2 |
| #23765158 | 2 |
| #23765147 | 2 |
| #23765108 | 2 |
| #23763525 | 2 |
| #23761514 | 2 |
| C79×#1381 | 2 |
| #12829 | 79 |