Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
450 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#19151414 | C2 | semidirect |
| 5. #26018368 | C2 | semidirect |
| 6. #26018356 | C2 | semidirect |
| 7. C89×#2141 | C2 | semidirect |
| 15. #19151870 | C4 | semidirect |
| 165. #2141 | D89 | semidirect |
| 169. C89 | #13069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033354 | 2 |
| C2×#19151870 | 2 |
| C2×#19151414 | 2 |
| #26020303 | 2 |
| #26018368 | 2 |
| #26018356 | 2 |
| C89×#2141 | 2 |
| #13069 | 89 |