Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
442 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×#19151428 | C2 | semidirect |
| 3. C2×#19151412 | C2 | semidirect |
| 4. #26021162 | C2 | semidirect |
| 5. C89×#2108 | C2 | semidirect |
| 10. C2×D1424 | C4 | semidirect |
| 121. #2108 | D89 | semidirect |
| 123. C89 | #13245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1424 | 2 |
| C2×#19151428 | 2 |
| C2×#19151412 | 2 |
| #26021162 | 2 |
| C89×#2108 | 2 |
| #13245 | 89 |