Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
252 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 71 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×#19151436 | C2 | semidirect |
| 2. C2×#19151433 | C2 | semidirect |
| 3. #26022513 | C2 | semidirect |
| 4. #26018386 | C2 | semidirect |
| 5. C89×#2246 | C2 | semidirect |
| 24. #15667918 | D4 | semidirect |
| 84. #2246 | D89 | semidirect |
| 86. C89 | #13729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151436 | 2 |
| C2×#19151433 | 2 |
| #26022513 | 2 |
| #26018386 | 2 |
| C89×#2246 | 2 |
| #13729 | 89 |