Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
692 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#19151909 | C2 | semidirect |
| 3. #26024723 | C2 | semidirect |
| 4. #26020336 | C2 | semidirect |
| 5. #26018819 | C2 | semidirect |
| 6. #26018100 | C2 | semidirect |
| 7. C89×#1964 | C2 | semidirect |
| 133. C22⋊C4×C89 | D8 | semidirect |
| 230. #1964 | D89 | semidirect |
| 234. C89 | #9952 | semidirect |
| 360. C22⋊C4 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031000 | 2 |
| C2×#19151909 | 2 |
| #26024723 | 2 |
| #26020336 | 2 |
| #26018819 | 2 |
| #26018100 | 2 |
| C89×#1964 | 2 |
| #9952 | 89 |