Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
202 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26018447 | C2 | semidirect |
| 4. C4×#15667918 | C2 | semidirect |
| 5. C4×C32×C89 | C2 | semidirect |
| 58. C4×D89 | C32 | semidirect |
| 84. C4×C32 | D89 | semidirect |
| 85. C89 | #13639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C16×D89 | 2 |
| #26018447 | 2 |
| #26018389 | 2 |
| C4×#15667918 | 2 |
| C4×C32×C89 | 2 |
| #13639 | 89 |