Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
120 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 47 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. #26018328 | C2 | semidirect |
| 3. C4×C32×C89 | C2 | semidirect |
| 59. C4×C32 | D89 | semidirect |
| 61. C89 | #7387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022134 | 2 |
| #26018328 | 2 |
| C4×C32×C89 | 2 |
| #7387 | 89 |