Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
560 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 39. #15667919 | Q8 | semidirect |
| 45. C22⋊C8×C89 | Q8 | semidirect |
| 194. C89 | #10568 | semidirect |
| 228. C22⋊C8 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026366 | 2 |
| #26020447 | 2 |
| #26018508 | 2 |
| #26018132 | 2 |
| C89×#1280 | 2 |
| #10568 | 89 |