Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
420 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26018890 | C2 | semidirect |
| 4. #26018655 | C2 | semidirect |
| 5. #26018121 | C2 | semidirect |
| 6. #26018113 | C2 | semidirect |
| 171. C89 | #9373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029328 | 2 |
| #26018947 | 2 |
| #26018890 | 2 |
| #26018655 | 2 |
| #26018121 | 2 |
| #26018113 | 2 |
| C89×#3216 | 2 |
| #9373 | 89 |