Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
224 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 68. C8×C89 | Q32 | semidirect |
| 88. C89 | #12494 | semidirect |
| 151. C8 | #15667958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022302 | 2 |
| #26019870 | 2 |
| #26018316 | 2 |
| #26018300 | 2 |
| C89×#1591 | 2 |
| #12494 | 89 |