Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
338 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 1. Q8×D632 | C2 | semidirect |
| 2. #23765623 | C2 | semidirect |
| 4. #23761456 | C2 | semidirect |
| 5. Q8⋊(C79⋊C16) | C2 | semidirect |
| 6. #23761360 | C2 | semidirect |
| 7. C79×#1668 | C2 | semidirect |
| 61. D632 | SD16 | semidirect |
| 89. Q8×C79 | D16 | semidirect |
| 140. #1668 | D79 | semidirect |
| 144. C79 | #12352 | semidirect |
| 229. Q8 | #14579102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D632 | 2 |
| #23765623 | 2 |
| #23765432 | 2 |
| #23761456 | 2 |
| Q8⋊(C79⋊C16) | 2 |
| #23761360 | 2 |
| C79×#1668 | 2 |
| #12352 | 79 |