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. #26018452 | C2 | semidirect |
| 4. #26018431 | C2 | semidirect |
| 5. C4×C32×C89 | C2 | semidirect |
| 8. D2848 | C4 | direct (N × H) |
| 17. D1424 | C2×C4 | semidirect |
| 24. C32×C89 | C2×C4 | semidirect |
| 53. C4×C89 | D32 | semidirect |
| 66. C4×C32 | D89 | semidirect |
| 67. C89 | C4×D32 | semidirect |
| 86. C32 | C4×D89 | semidirect |
| 116. C4 | D2848 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D2848 | 2 |
| C4×D1424 | 2 |
| #26018452 | 2 |
| #26018431 | 2 |
| C4×C32×C89 | 2 |
| C4×D32 | 89 |