Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
354 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 354 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. #26022171 | C2 | semidirect |
| 3. #26022168 | C2 | semidirect |
| 4. #26021521 | C2 | semidirect |
| 5. #26018266 | C2 | semidirect |
| 6. #26018193 | C2 | semidirect |
| 7. C89×#1349 | C2 | semidirect |
| 171. #1349 | D89 | semidirect |
| 173. C89 | #12167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031686 | 2 |
| #26022171 | 2 |
| #26022168 | 2 |
| #26021521 | 2 |
| #26018266 | 2 |
| #26018193 | 2 |
| C89×#1349 | 2 |
| #12167 | 89 |