Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1160 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 117 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×#19151732 | C2 | semidirect |
| 2. #26026356 | C2 | semidirect |
| 3. C2×#19151333 | C2 | semidirect |
| 4. C2×#19151332 | C2 | semidirect |
| 5. #26018493 | C2 | semidirect |
| 6. #26018094 | C2 | semidirect |
| 7. C2×#447×C89 | C2 | semidirect |
| 55. C22⋊#10623494 | D4 | semidirect |
| 69. C22×D4×C89 | D4 | semidirect |
| 82. C22⋊C8×C89 | D4 | semidirect |
| 104. C22×Dic89 | D8 | semidirect |
| 299. C2×#447 | D89 | semidirect |
| 305. C89 | #9962 | semidirect |
| 341. C22×D4 | C22⋊D89 | semidirect |
| 376. C22⋊C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151732 | 2 |
| #26026356 | 2 |
| C2×#19151333 | 2 |
| C2×#19151332 | 2 |
| #26018493 | 2 |
| #26018094 | 2 |
| C2×#447×C89 | 2 |
| #9962 | 89 |