Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
212 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 212 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. #26018324 | C2 | semidirect |
| 4. #26018310 | C2 | semidirect |
| 5. C89×#2252 | C2 | semidirect |
| 81. #2252 | D89 | semidirect |
| 86. C89 | #12452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D356 | 2 |
| #26019648 | 2 |
| #26018324 | 2 |
| #26018310 | 2 |
| C89×#2252 | 2 |
| #12452 | 89 |