Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
398 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26022502 | C2 | semidirect |
| 2. #26022501 | C2 | semidirect |
| 3. #26019866 | C2 | semidirect |
| 4. C16×#10623494 | C2 | semidirect |
| 5. C89×#2246 | C2 | semidirect |
| 35. #13083549 | D8 | semidirect |
| 43. C16×C89 | D8 | semidirect |
| 56. #10623494 | D16 | semidirect |
| 72. #2246 | D89 | semidirect |
| 75. C89 | #12515 | semidirect |
| 113. C16 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022502 | 2 |
| #26022501 | 2 |
| #26019866 | 2 |
| C16×#10623494 | 2 |
| C89×#2246 | 2 |
| #12515 | 89 |