Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26022161 | C2 | semidirect |
| 4. #26018315 | C2 | semidirect |
| 6. C16×#10623494 | C2 | semidirect |
| 7. C89×Q8⋊C16 | C2 | semidirect |
| 57. #13083549 | SD16 | semidirect |
| 88. #10623494 | M32 | semidirect |
| 110. Q8⋊C16 | D89 | semidirect |
| 113. C89 | #12051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022161 | 2 |
| #26022083 | 2 |
| C8×#13083561 | 2 |
| #26018315 | 2 |
| #26018208 | 2 |
| C16×#10623494 | 2 |
| C89×Q8⋊C16 | 2 |
| #12051 | 89 |