Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
576 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 7. C22×C4×Dic89 | C4 | semidirect |
| 12. #19151470 | C4 | semidirect |
| 13. #19151459 | C4 | semidirect |
| 17. C4×C22⋊Dic89 | C4 | semidirect |
| 18. #19151389 | C4 | direct (N × H) |
| 73. C22×Dic89 | C42 | semidirect |
| 82. C22⋊Dic89 | C42 | semidirect |
| 185. C4×C89 | #352 | semidirect |
| 205. C89 | C4×#352 | semidirect |
| 390. C4 | #19151389 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667993 | 2 |
| C2×#19151389 | 2 |
| C4×#15667927 | 2 |
| #26018371 | 2 |
| C4×#100×C89 | 2 |
| C4×#352 | 89 |