Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
406 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26018417 | C2 | semidirect |
| 9. C2×C4⋊Q8×C89 | C4 | semidirect |
| 11. #494×C89 | C4 | semidirect |
| 13. C4×M16×C89 | C4 | semidirect |
| 106. C89 | #13586 | semidirect |
| 109. C2×C4⋊Q8 | Dic89 | semidirect |
| 111. #494 | Dic89 | semidirect |
| 114. C4×M16 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021917 | 2 |
| #26018417 | 2 |
| C89×#3152 | 2 |
| #13586 | 89 |