Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
348 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 5. #19151391 | C4 | semidirect |
| 8. C2×C4×C8×C89 | C4 | semidirect |
| 9. #384×C89 | C4 | semidirect |
| 105. C89 | #7498 | semidirect |
| 109. C2×C4×C8 | Dic89 | semidirect |
| 110. #384 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151391 | 2 |
| C89×#1957 | 2 |
| #7498 | 89 |