Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
214 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 67 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. C2×D2848 | C2 | semidirect |
| 2. #26022338 | C2 | semidirect |
| 3. #26018452 | C2 | semidirect |
| 4. #26018431 | C2 | semidirect |
| 5. C22×C32×C89 | C2 | semidirect |
| 27. C32×C89 | D4 | semidirect |
| 57. C22×C89 | D32 | semidirect |
| 73. C22×C32 | D89 | semidirect |
| 77. C89 | #13694 | semidirect |
| 99. C32 | C22⋊D89 | semidirect |
| 132. C22 | D2848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D2848 | 2 |
| #26022338 | 2 |
| #26018452 | 2 |
| #26018431 | 2 |
| C22×C32×C89 | 2 |
| #13694 | 89 |