Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
376 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 87 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. #19151365 | C4 | semidirect |
| 7. C2×C4⋊C8×C89 | C4 | semidirect |
| 9. C2×C4×C8×C89 | C4 | semidirect |
| 115. C89 | #7237 | semidirect |
| 117. C2×C4⋊C8 | Dic89 | semidirect |
| 120. C2×C4×C8 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020240 | 2 |
| C89×#1954 | 2 |
| #7237 | 89 |