Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
168 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 53 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. #26018451 | C2 | semidirect |
| 4. #26018434 | C2 | semidirect |
| 5. #26018432 | C2 | semidirect |
| 7. C89×#1424 | C2 | semidirect |
| 86. #1424 | D89 | semidirect |
| 91. C89 | #13716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022344 | 2 |
| #26022033 | 2 |
| #26018451 | 2 |
| #26018434 | 2 |
| #26018432 | 2 |
| #26018389 | 2 |
| C89×#1424 | 2 |
| #13716 | 89 |