Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
466 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 135 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. #23765027 | C2 | semidirect |
| 3. #23765021 | C2 | semidirect |
| 4. #23761479 | C2 | semidirect |
| 5. C79×#3407 | C2 | semidirect |
| 54. C2×C16×C79 | D4 | semidirect |
| 143. #3407 | D79 | semidirect |
| 148. C79 | #12988 | semidirect |
| 192. C2×C16 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772116 | 2 |
| #23765027 | 2 |
| #23765021 | 2 |
| #23761479 | 2 |
| C79×#3407 | 2 |
| #12988 | 79 |