Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
230 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. C4⋊#15667918 | C2 | semidirect |
| 4. #26018447 | C2 | semidirect |
| 5. C89×C4⋊C32 | C2 | semidirect |
| 59. C4×D89 | C32 | semidirect |
| 72. C4×C89 | C2×C32 | semidirect |
| 77. Dic89 | C2×C32 | semidirect |
| 82. D89 | C4⋊C32 | direct (N × H) |
| 87. C4⋊C32 | D89 | direct (N × H) |
| 88. C89 | C2×C4⋊C32 | semidirect |
| 158. C4 | C32×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D89 | 2 |
| C4×C16×D89 | 2 |
| C4⋊#15667918 | 2 |
| #26018447 | 2 |
| C89×C4⋊C32 | 2 |
| C2×C4⋊C32 | 89 |