Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
630 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 139 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. #26018644 | C2 | semidirect |
| 3. #26018573 | C2 | semidirect |
| 4. #26018080 | C2 | semidirect |
| 5. C89×#2972 | C2 | semidirect |
| 25. #15668008 | C8 | semidirect |
| 51. C4×C8×C89 | D4 | semidirect |
| 56. C2×D356 | C2×C8 | semidirect |
| 73. C4×Dic89 | C2×C8 | semidirect |
| 164. #2972 | D89 | semidirect |
| 169. C89 | #9101 | semidirect |
| 212. C4×C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022974 | 2 |
| #26018644 | 2 |
| #26018573 | 2 |
| #26018080 | 2 |
| C89×#2972 | 2 |
| #9101 | 89 |