Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
258 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. C8×D712 | C2 | semidirect |
| 3. #26018324 | C2 | semidirect |
| 4. #26018214 | C2 | semidirect |
| 5. C8×C16×C89 | C2 | semidirect |
| 19. D1424 | C8 | direct (N × H) |
| 33. D712 | C2×C8 | semidirect |
| 46. C16×C89 | C2×C8 | semidirect |
| 59. C8×C89 | D16 | semidirect |
| 82. C8×C16 | D89 | semidirect |
| 83. C89 | C8×D16 | semidirect |
| 124. C16 | C8×D89 | semidirect |
| 138. C8 | D1424 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1424 | 2 |
| C8×D712 | 2 |
| #26018324 | 2 |
| #26018214 | 2 |
| C8×C16×C89 | 2 |
| C8×D16 | 89 |