Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×Dic1424 | C2 | semidirect |
| 3. C2×#19151438 | C2 | semidirect |
| 4. Q64×D89 | C2 | direct (N × H) |
| 6. C2×Q64×C89 | C2 | semidirect |
| 13. Dic1424 | C22 | semidirect |
| 14. #19151438 | C22 | semidirect |
| 18. Q64×C89 | C22 | semidirect |
| 74. C2×D89 | Q64 | direct (N × H) |
| 82. C2×C89 | C2×Q64 | semidirect |
| 84. D89 | C2×Q64 | direct (N × H) |
| 89. C2×Q64 | D89 | direct (N × H) |
| 91. C89 | C22×Q64 | semidirect |
| 101. Q64 | C2×D89 | direct (N × H) |
| 167. C2 | Q64×D89 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D89 | 2 |
| C2×Dic1424 | 2 |
| C2×#19151438 | 2 |
| Q64×D89 | 2 |
| C2×C32×D89 | 2 |
| C2×Q64×C89 | 2 |
| C22×Q64 | 89 |