Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
534 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26018803 | C2 | semidirect |
| 4. #26018117 | C2 | semidirect |
| 15. #486×C89 | C4 | semidirect |
| 30. C4⋊Q8×C89 | C2×C4 | semidirect |
| 41. C4×C8×C89 | C2×C4 | semidirect |
| 117. C89 | #9425 | semidirect |
| 121. #486 | Dic89 | semidirect |
| 134. C4⋊Q8 | C2×Dic89 | semidirect |
| 150. C4×C8 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023429 | 2 |
| #26018966 | 2 |
| #26018803 | 2 |
| #26018117 | 2 |
| C89×#3138 | 2 |
| #9425 | 89 |