Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
284 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #26022534 | C2 | semidirect |
| 3. #26022480 | C2 | semidirect |
| 5. #26019849 | C2 | semidirect |
| 7. C8×C16×C89 | C2 | semidirect |
| 68. C16×C89 | SD16 | semidirect |
| 85. C8×C89 | SD32 | semidirect |
| 110. C8×C16 | D89 | semidirect |
| 111. C89 | #12505 | semidirect |
| 172. C16 | #13083563 | semidirect |
| 189. C8 | #15667957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022534 | 2 |
| #26022508 | 2 |
| #26022480 | 2 |
| #26022476 | 2 |
| #26019849 | 2 |
| #26019844 | 2 |
| C8×C16×C89 | 2 |
| #12505 | 89 |