Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
542 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 115 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×#19151340 | C2 | semidirect |
| 4. #26018133 | C2 | semidirect |
| 5. C89×#2382 | C2 | semidirect |
| 8. #19151964 | C4 | semidirect |
| 137. #2382 | D89 | semidirect |
| 141. C89 | #9002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151964 | 2 |
| #26021075 | 2 |
| C2×#19151340 | 2 |
| #26018133 | 2 |
| C89×#2382 | 2 |
| #9002 | 89 |