Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
506 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 506 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 |
|---|---|---|
| 1. #23776406 | C2 | semidirect |
| 3. #23765628 | C2 | semidirect |
| 4. #23765543 | C2 | semidirect |
| 7. Q8×C16×C79 | C2 | semidirect |
| 72. Q8×C79 | SD32 | semidirect |
| 109. Q8×C16 | D79 | semidirect |
| 111. C79 | #33926 | semidirect |
| 179. Q8 | #14579106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776406 | 2 |
| Q8×D632 | 2 |
| #23765628 | 2 |
| #23765543 | 2 |
| #23765446 | 2 |
| C4×#14579106 | 2 |
| Q8×C16×C79 | 2 |
| #33926 | 79 |