Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
416 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 24. #15668012 | Q8 | semidirect |
| 25. #15668012 | Q8 | semidirect |
| 161. C89 | #10363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028628 | 2 |
| #26021228 | 2 |
| #26018817 | 2 |
| #26018815 | 2 |
| #26018112 | 2 |
| #26018084 | 2 |
| C89×#1286 | 2 |
| #10363 | 89 |