Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
306 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26022394 | C2 | semidirect |
| 4. #26019647 | C2 | semidirect |
| 6. #26018232 | C2 | semidirect |
| 7. C89×#1332 | C2 | semidirect |
| 135. #1332 | D89 | semidirect |
| 136. C89 | #12381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033262 | 2 |
| #26022476 | 2 |
| #26022394 | 2 |
| #26019647 | 2 |
| #26018297 | 2 |
| #26018232 | 2 |
| C89×#1332 | 2 |
| #12381 | 89 |