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. #26021176 | C2 | semidirect |
| 4. #26019004 | C2 | semidirect |
| 6. #26018153 | C2 | semidirect |
| 7. C89×#1997 | C2 | semidirect |
| 107. M16×C89 | SD16 | semidirect |
| 188. #1997 | D89 | semidirect |
| 194. C89 | #10501 | semidirect |
| 282. M16 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031177 | 2 |
| #26021176 | 2 |
| #26021171 | 2 |
| #26019004 | 2 |
| #26018930 | 2 |
| #26018153 | 2 |
| C89×#1997 | 2 |
| #10501 | 89 |