Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
288 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 88. Q8×C89 | Q32 | semidirect |
| 128. C89 | #12358 | semidirect |
| 211. Q8 | #15667958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022481 | 2 |
| #26022302 | 2 |
| #26019622 | 2 |
| #26018310 | 2 |
| Q8⋊#13083549 | 2 |
| #26018216 | 2 |
| Q8×Q16×C89 | 2 |
| #12358 | 89 |