Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
384 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26019015 | C2 | semidirect |
| 3. #26018853 | C2 | semidirect |
| 5. #26018607 | C2 | semidirect |
| 7. C89×#1451 | C2 | semidirect |
| 181. #1451 | D89 | semidirect |
| 182. C89 | #9790 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151953 | 2 |
| #26019015 | 2 |
| #26018853 | 2 |
| #26018849 | 2 |
| #26018607 | 2 |
| #26018603 | 2 |
| C89×#1451 | 2 |
| #9790 | 89 |