Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 16. #19151397 | C4 | semidirect |
| 20. #356×C89 | C4 | semidirect |
| 145. Dic89 | #356 | direct (N × H) |
| 157. C89 | C4×#356 | semidirect |
| 171. #356 | Dic89 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×Dic89 | 2 |
| C2×#19151397 | 2 |
| #101×Dic89 | 2 |
| #26018378 | 2 |
| C2×#356×C89 | 2 |
| C4×#356 | 89 |