Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
528 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26018655 | C2 | semidirect |
| 4. #26018083 | C2 | semidirect |
| 5. C89×#3162 | C2 | semidirect |
| 72. C2×C8×C89 | SD16 | semidirect |
| 134. #3162 | D89 | semidirect |
| 139. C89 | #10036 | semidirect |
| 204. C2×C8 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030256 | 2 |
| #26021050 | 2 |
| #26018655 | 2 |
| #26018083 | 2 |
| C89×#3162 | 2 |
| #10036 | 89 |