Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
232 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 232 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×#19151438 | C2 | semidirect |
| 4. #26018386 | C2 | semidirect |
| 5. C89×#2247 | C2 | semidirect |
| 81. #2247 | D89 | semidirect |
| 83. C89 | #13730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151438 | 2 |
| C2×#19151435 | 2 |
| #26022513 | 2 |
| #26018386 | 2 |
| C89×#2247 | 2 |
| #13730 | 89 |