Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
850 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 850 conjugacy classes of subgroups — too many to draw. Only its 171 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. #23763517 | C2 | semidirect |
| 3. C2×#19098306 | C2 | semidirect |
| 4. C79×#1767 | C2 | semidirect |
| 38. C4⋊C8×C79 | D4 | semidirect |
| 129. #1767 | D79 | semidirect |
| 131. C79 | #9706 | semidirect |
| 165. C4⋊C8 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771795 | 2 |
| #23763517 | 2 |
| C2×#19098306 | 2 |
| C79×#1767 | 2 |
| #9706 | 79 |