Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
354 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 97. C2×C4×C89 | Q32 | semidirect |
| 132. C89 | #12162 | semidirect |
| 229. C2×C4 | #15667958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031597 | 2 |
| #26022186 | 2 |
| #26018263 | 2 |
| #26018192 | 2 |
| C89×#2056 | 2 |
| #12162 | 89 |