Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
244 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23765308 | C2 | semidirect |
| 3. #23762761 | C2 | semidirect |
| 4. #23761445 | C2 | semidirect |
| 5. C79×#1372 | C2 | semidirect |
| 51. C16×C79 | SD16 | semidirect |
| 87. #1372 | D79 | semidirect |
| 89. C79 | #12442 | semidirect |
| 135. C16 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765650 | 2 |
| #23765308 | 2 |
| #23762761 | 2 |
| #23761445 | 2 |
| C79×#1372 | 2 |
| #12442 | 79 |