Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
488 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #26018199 | C2 | semidirect |
| 4. #26018181 | C2 | semidirect |
| 27. #15667993 | C8 | semidirect |
| 67. C22×Dic89 | C2×C8 | semidirect |
| 76. C22⋊Dic89 | C2×C8 | semidirect |
| 193. C89 | #11472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667993 | 2 |
| #26018570 | 2 |
| #26018199 | 2 |
| #26018181 | 2 |
| C89×#1460 | 2 |
| #11472 | 89 |