Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
722 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 722 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. C2×#19151780 | C2 | semidirect |
| 3. C2×#19151397 | C2 | semidirect |
| 4. C2×#19151395 | C2 | semidirect |
| 5. #26020210 | C2 | semidirect |
| 6. #26018379 | C2 | semidirect |
| 7. C89×#2731 | C2 | semidirect |
| 284. #2731 | D89 | semidirect |
| 289. C89 | #13358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151780 | 2 |
| C2×#19151770 | 2 |
| C2×#19151397 | 2 |
| C2×#19151395 | 2 |
| #26020210 | 2 |
| #26018379 | 2 |
| C89×#2731 | 2 |
| #13358 | 89 |