Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #26022564 | C2 | semidirect |
| 2. #26022500 | C2 | semidirect |
| 3. #26022133 | C2 | semidirect |
| 4. #26018449 | C2 | semidirect |
| 5. #26018443 | C2 | semidirect |
| 6. #26018442 | C2 | semidirect |
| 7. C89×#2263 | C2 | semidirect |
| 37. Q32×C89 | D4 | semidirect |
| 41. D16×C89 | D4 | semidirect |
| 101. #2263 | D89 | semidirect |
| 107. C89 | #13692 | semidirect |
| 129. Q32 | C22⋊D89 | semidirect |
| 136. D16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022564 | 2 |
| #26022500 | 2 |
| #26022133 | 2 |
| #26018449 | 2 |
| #26018443 | 2 |
| #26018442 | 2 |
| C89×#2263 | 2 |
| #13692 | 89 |