Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
126 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 126 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 |
|---|---|---|
| 16. Q32×C89 | C8 | semidirect |
| 61. C89 | #7384 | semidirect |
| 72. Q32 | #10623494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667918 | 2 |
| #26018324 | 2 |
| C4×Q32×C89 | 2 |
| #7384 | 89 |