Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
196 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 24. C2×Q8×C89 | C16 | semidirect |
| 82. C89 | #7057 | semidirect |
| 103. C2×Q8 | #13083549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018192 | 2 |
| C89×#1984 | 2 |
| #7057 | 89 |