Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
248 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 71 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. Q8×C79⋊C16 | C2 | semidirect |
| 3. #23762760 | C2 | semidirect |
| 4. #23761471 | C2 | semidirect |
| 5. #23761446 | C2 | semidirect |
| 6. #23761445 | C2 | semidirect |
| 7. C79×#1668 | C2 | semidirect |
| 55. C79⋊C16 | SD16 | semidirect |
| 75. Q8×C79 | D16 | semidirect |
| 120. #1668 | D79 | semidirect |
| 124. C79 | #12439 | semidirect |
| 192. Q8 | #14579102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765649 | 2 |
| Q8×C79⋊C16 | 2 |
| #23762760 | 2 |
| #23761471 | 2 |
| #23761446 | 2 |
| #23761445 | 2 |
| C79×#1668 | 2 |
| #12439 | 79 |