Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
440 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26021241 | C2 | semidirect |
| 3. #26021174 | C2 | semidirect |
| 6. #26018154 | C2 | semidirect |
| 7. C89×#1565 | C2 | semidirect |
| 108. M16×C89 | SD16 | semidirect |
| 191. #1565 | D89 | semidirect |
| 194. C89 | #10501 | semidirect |
| 282. M16 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031179 | 2 |
| #26021241 | 2 |
| #26021174 | 2 |
| #26021171 | 2 |
| #26018927 | 2 |
| #26018154 | 2 |
| C89×#1565 | 2 |
| #10501 | 89 |