Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
372 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26022049 | C2 | semidirect |
| 3. #26019009 | C2 | semidirect |
| 4. #26018217 | C2 | semidirect |
| 5. #26018215 | C2 | semidirect |
| 6. #26018213 | C2 | semidirect |
| 7. C89×#1331 | C2 | semidirect |
| 72. Dic356 | M16 | semidirect |
| 96. D8×C89 | M16 | semidirect |
| 166. #1331 | D89 | semidirect |
| 167. C89 | #11660 | semidirect |
| 237. D8 | #13083557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668031 | 2 |
| #26022049 | 2 |
| #26019009 | 2 |
| #26018217 | 2 |
| #26018215 | 2 |
| #26018213 | 2 |
| C89×#1331 | 2 |
| #11660 | 89 |