Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 284 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. #26022481 | C2 | semidirect |
| 4. #26019850 | C2 | semidirect |
| 6. C16×#10623494 | C2 | semidirect |
| 7. C89×#2254 | C2 | semidirect |
| 68. C16×C89 | SD16 | semidirect |
| 87. #10623494 | SD32 | semidirect |
| 104. #2254 | D89 | semidirect |
| 111. C89 | #12505 | semidirect |
| 172. C16 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022508 | 2 |
| #26022481 | 2 |
| #26022477 | 2 |
| #26019850 | 2 |
| #26019845 | 2 |
| C16×#10623494 | 2 |
| C89×#2254 | 2 |
| #12505 | 89 |