Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
216 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26022502 | C2 | semidirect |
| 3. #26018450 | C2 | semidirect |
| 4. #26018441 | C2 | semidirect |
| 5. C89×#2178 | C2 | semidirect |
| 26. Q32×C89 | D4 | semidirect |
| 28. D16×C89 | D4 | semidirect |
| 83. #2178 | D89 | semidirect |
| 86. C89 | #13692 | semidirect |
| 103. Q32 | D356 | semidirect |
| 108. D16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022564 | 2 |
| #26022502 | 2 |
| #26018450 | 2 |
| #26018441 | 2 |
| C89×#2178 | 2 |
| #13692 | 89 |