Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
726 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 2. #26020369 | C2 | semidirect |
| 3. C2×#19151327 | C2 | semidirect |
| 4. C4×#97×C89 | C2 | semidirect |
| 38. C4×C8×C89 | D4 | semidirect |
| 125. C4×#97 | D89 | semidirect |
| 127. C89 | #9648 | semidirect |
| 161. C4×C8 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668009 | 2 |
| #26020369 | 2 |
| C2×#19151327 | 2 |
| C4×#97×C89 | 2 |
| #9648 | 89 |