Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
664 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 159 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. C2×Q32×D89 | C2 | semidirect |
| 3. #26022505 | C2 | semidirect |
| 4. #26022344 | C2 | semidirect |
| 5. #26022302 | C2 | semidirect |
| 6. #26022187 | C2 | semidirect |
| 8. C4×Q32×C89 | C2 | semidirect |
| 52. Q32×C89 | D4 | semidirect |
| 100. D356 | Q32 | direct (N × H) |
| 114. C2×D89 | C2×Q32 | semidirect |
| 118. C4×C89 | C2×Q32 | semidirect |
| 134. C4×Q32 | D89 | semidirect |
| 136. C89 | D4×Q32 | semidirect |
| 175. Q32 | D356 | direct (N × H) |
| 248. C4 | Q32×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D89 | 2 |
| Q16×D356 | 2 |
| #26022505 | 2 |
| #26022344 | 2 |
| #26022302 | 2 |
| #26022187 | 2 |
| C16×D356 | 2 |
| C4×Q32×C89 | 2 |
| D4×Q32 | 89 |