Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26019071 | C2 | semidirect |
| 4. #26018317 | C2 | semidirect |
| 6. #26018172 | C2 | semidirect |
| 7. C89×#1334 | C2 | semidirect |
| 58. Q16×C89 | M16 | semidirect |
| 107. #1334 | D89 | semidirect |
| 110. C89 | #12080 | semidirect |
| 151. Q16 | #13083557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022114 | 2 |
| #26019165 | 2 |
| #26019071 | 2 |
| #26018317 | 2 |
| #26018220 | 2 |
| #26018172 | 2 |
| C89×#1334 | 2 |
| #12080 | 89 |