Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 256 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. #23762993 | C2 | semidirect |
| 3. D8×C79⋊C8 | C2 | semidirect |
| 4. #23761463 | C2 | semidirect |
| 5. #23761458 | C2 | semidirect |
| 6. #23761447 | C2 | semidirect |
| 7. C79×#2226 | C2 | semidirect |
| 62. D8×C79 | SD16 | semidirect |
| 115. #2226 | D79 | semidirect |
| 122. C79 | #12418 | semidirect |
| 171. D8 | #11929611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765435 | 2 |
| #23762993 | 2 |
| D8×C79⋊C8 | 2 |
| #23761463 | 2 |
| #23761458 | 2 |
| #23761447 | 2 |
| C79×#2226 | 2 |
| #12418 | 79 |