Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #26032683 | C2 | semidirect |
| 2. #26022475 | C2 | semidirect |
| 3. #26022289 | C2 | semidirect |
| 4. #26018308 | C2 | semidirect |
| 5. #26018215 | C2 | semidirect |
| 6. D4⋊#13083549 | C2 | semidirect |
| 142. C89 | #12341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26032683 | 2 |
| #26022475 | 2 |
| #26022289 | 2 |
| #26018308 | 2 |
| #26018215 | 2 |
| D4⋊#13083549 | 2 |
| C89×#1667 | 2 |
| #12341 | 89 |