Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
358 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23762159 | C2 | semidirect |
| 3. #23761454 | C2 | semidirect |
| 4. #23761447 | C2 | semidirect |
| 5. C2×C4⋊C16×C79 | C2 | semidirect |
| 131. C2×C4⋊C16 | D79 | semidirect |
| 135. C79 | #11981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773979 | 2 |
| #23762159 | 2 |
| #23761454 | 2 |
| #23761447 | 2 |
| C2×C4⋊C16×C79 | 2 |
| #11981 | 79 |