Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
140 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 140 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 |
|---|---|---|
| 27. Q16×C89 | C16 | semidirect |
| 67. C89 | #7071 | semidirect |
| 89. Q16 | #13083549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018316 | 2 |
| #26018170 | 2 |
| C8×Q16×C89 | 2 |
| #7071 | 89 |