Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
304 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 304 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×Dic316 | C2 | semidirect |
| 4. #23761459 | C2 | semidirect |
| 5. Q8⋊(C79⋊C16) | C2 | semidirect |
| 6. #23761363 | C2 | semidirect |
| 57. Dic316 | SD16 | semidirect |
| 86. Q8×C79 | SD32 | semidirect |
| 135. C79 | #12354 | semidirect |
| 218. Q8 | #14579105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic316 | 2 |
| #23765623 | 2 |
| #23765437 | 2 |
| #23761459 | 2 |
| Q8⋊(C79⋊C16) | 2 |
| #23761363 | 2 |
| C79×#1668 | 2 |
| #12354 | 79 |