Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
226 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 226 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. #26019149 | C2 | semidirect |
| 3. #26018326 | C2 | semidirect |
| 4. #26018216 | C2 | semidirect |
| 6. #26018171 | C2 | semidirect |
| 88. #10623494 | SD32 | semidirect |
| 113. C89 | #12070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26019149 | 2 |
| D8×#10623494 | 2 |
| #26018326 | 2 |
| #26018216 | 2 |
| #26018213 | 2 |
| #26018171 | 2 |
| C4×SD32×C89 | 2 |
| #12070 | 89 |