Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
428 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26019010 | C2 | semidirect |
| 5. C2×Q8⋊#10623494 | C2 | semidirect |
| 6. #26018126 | C2 | semidirect |
| 7. C89×#1801 | C2 | semidirect |
| 190. #1801 | D89 | semidirect |
| 196. C89 | #10458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029724 | 2 |
| #26019010 | 2 |
| #26018930 | 2 |
| #26018702 | 2 |
| C2×Q8⋊#10623494 | 2 |
| #26018126 | 2 |
| C89×#1801 | 2 |
| #10458 | 89 |