Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
464 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26021604 | C2 | semidirect |
| 4. #26018252 | C2 | semidirect |
| 6. #26018199 | C2 | semidirect |
| 7. C89×#1608 | C2 | semidirect |
| 89. C22⋊Dic89 | SD16 | semidirect |
| 205. #1608 | D89 | semidirect |
| 210. C89 | #12243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026756 | 2 |
| #26021604 | 2 |
| #26019175 | 2 |
| #26018252 | 2 |
| #26018250 | 2 |
| #26018199 | 2 |
| C89×#1608 | 2 |
| #12243 | 89 |