Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
228 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26019622 | C2 | semidirect |
| 4. #26018324 | C2 | semidirect |
| 5. #26018302 | C2 | semidirect |
| 7. C89×#2183 | C2 | semidirect |
| 70. C16×C89 | SD16 | semidirect |
| 111. #2183 | D89 | semidirect |
| 117. C89 | #12444 | semidirect |
| 180. C16 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022508 | 2 |
| #26019622 | 2 |
| #26019612 | 2 |
| #26018324 | 2 |
| #26018302 | 2 |
| #26018299 | 2 |
| C89×#2183 | 2 |
| #12444 | 89 |