Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
706 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 219 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. #26019869 | C2 | semidirect |
| 4. #26019861 | C2 | semidirect |
| 5. #26019847 | C2 | semidirect |
| 69. C2×C8×C89 | Q16 | semidirect |
| 115. C89 | #19604 | semidirect |
| 172. C2×C8 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030834 | 2 |
| #26030766 | 2 |
| #26019869 | 2 |
| #26019861 | 2 |
| #26019847 | 2 |
| C2×C8×#10623494 | 2 |
| C89×#3160 | 2 |
| #19604 | 89 |