Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26022053 | C2 | semidirect |
| 3. #26019006 | C2 | semidirect |
| 4. #26018223 | C2 | semidirect |
| 5. #26018221 | C2 | semidirect |
| 6. #26018219 | C2 | semidirect |
| 7. C89×#1333 | C2 | semidirect |
| 72. Dic356 | M16 | semidirect |
| 96. D8×C89 | M16 | semidirect |
| 163. #1333 | D89 | semidirect |
| 164. C89 | #11666 | semidirect |
| 234. 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 |
| #26022053 | 2 |
| #26019006 | 2 |
| #26018223 | 2 |
| #26018221 | 2 |
| #26018219 | 2 |
| C89×#1333 | 2 |
| #11666 | 89 |