Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
210 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 85. #10623494 | Q32 | semidirect |
| 107. C89 | #12072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26019149 | 2 |
| Q16×#10623494 | 2 |
| #26018324 | 2 |
| #26018216 | 2 |
| #26018171 | 2 |
| C4×Q32×C89 | 2 |
| #12072 | 89 |