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 |
|---|---|---|
| 28. #15668012 | Q8 | semidirect |
| 29. #15668012 | Q8 | semidirect |
| 186. C89 | #10371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023546 | 2 |
| #26021232 | 2 |
| #26018752 | 2 |
| #26018750 | 2 |
| #26018153 | 2 |
| #26018080 | 2 |
| C89×#1303 | 2 |
| #10371 | 89 |