Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
214 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 75 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. C4×D1424 | C2 | semidirect |
| 3. #26018451 | C2 | semidirect |
| 4. #26018430 | C2 | semidirect |
| 5. #26018429 | C2 | semidirect |
| 6. C4×#15667918 | C2 | semidirect |
| 7. C4×D16×C89 | C2 | semidirect |
| 10. #19151433 | C4 | direct (N × H) |
| 23. D1424 | C2×C4 | semidirect |
| 27. #15667918 | C2×C4 | semidirect |
| 31. D16×C89 | C2×C4 | semidirect |
| 80. C4×C89 | D32 | semidirect |
| 92. C4×D16 | D89 | semidirect |
| 97. C89 | C4×D32 | semidirect |
| 117. D16 | C4×D89 | semidirect |
| 171. C4 | #19151433 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151433 | 2 |
| C4×D1424 | 2 |
| #26018451 | 2 |
| #26018430 | 2 |
| #26018429 | 2 |
| C4×#15667918 | 2 |
| C4×D16×C89 | 2 |
| C4×D32 | 89 |