Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
528 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 165 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×Dic316 | C2 | semidirect |
| 3. #23765624 | C2 | semidirect |
| 4. #23765548 | C2 | semidirect |
| 5. #23765441 | C2 | semidirect |
| 6. C4×#14579106 | C2 | semidirect |
| 7. Q8×C16×C79 | C2 | semidirect |
| 54. Dic316 | #41 | semidirect |
| 72. Q8×C79 | SD32 | semidirect |
| 111. Q8×C16 | D79 | semidirect |
| 113. C79 | #33929 | semidirect |
| 181. Q8 | #14579106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776375 | 2 |
| Q8×Dic316 | 2 |
| #23765624 | 2 |
| #23765548 | 2 |
| #23765441 | 2 |
| C4×#14579106 | 2 |
| Q8×C16×C79 | 2 |
| #33929 | 79 |