Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
360 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 28. #15668012 | Q8 | semidirect |
| 29. #15668012 | Q8 | semidirect |
| 172. C89 | #10379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021195 | 2 |
| #26018802 | 2 |
| #26018763 | 2 |
| #26018145 | 2 |
| #26018116 | 2 |
| #26018108 | 2 |
| C89×#2605 | 2 |
| #10379 | 89 |