Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 3. #23761470 | C2 | semidirect |
| 4. #23761458 | C2 | semidirect |
| 5. C79×#1713 | C2 | semidirect |
| 37. D632 | Q16 | semidirect |
| 88. #1713 | D79 | semidirect |
| 92. C79 | #12447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765544 | 2 |
| C8×D632 | 2 |
| #23761470 | 2 |
| #23761458 | 2 |
| C79×#1713 | 2 |
| #12447 | 79 |