Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
524 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26021201 | C2 | semidirect |
| 5. #26018751 | C2 | semidirect |
| 6. #26018103 | C2 | semidirect |
| 7. C89×#3165 | C2 | semidirect |
| 107. M16×C89 | SD16 | semidirect |
| 191. #3165 | D89 | semidirect |
| 196. C89 | #10197 | semidirect |
| 286. M16 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031564 | 2 |
| #26031177 | 2 |
| #26021201 | 2 |
| #26021171 | 2 |
| #26018751 | 2 |
| #26018103 | 2 |
| C89×#3165 | 2 |
| #10197 | 89 |