Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
242 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. #26018326 | C2 | semidirect |
| 4. #26018323 | C2 | semidirect |
| 5. C89×#1372 | C2 | semidirect |
| 23. C16×D89 | C8 | semidirect |
| 91. #1372 | D89 | semidirect |
| 93. C89 | #12008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C16×D89 | 2 |
| #26018999 | 2 |
| #26018326 | 2 |
| #26018323 | 2 |
| C89×#1372 | 2 |
| #12008 | 89 |