Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
180 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26018432 | C2 | semidirect |
| 4. C4×#15667918 | C2 | semidirect |
| 5. C89×#2253 | C2 | semidirect |
| 68. #2253 | D89 | semidirect |
| 73. C89 | #13721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022513 | 2 |
| #26018432 | 2 |
| #26018429 | 2 |
| C4×#15667918 | 2 |
| C89×#2253 | 2 |
| #13721 | 89 |