Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
580 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #26020533 | C2 | semidirect |
| 5. #26018370 | C2 | semidirect |
| 6. #26018369 | C2 | semidirect |
| 7. C89×#1867 | C2 | semidirect |
| 20. #19151390 | C4 | semidirect |
| 51. #15667927 | C2×C4 | semidirect |
| 70. #99×C89 | C2×C4 | semidirect |
| 77. C2×D356 | C4⋊C4 | semidirect |
| 107. C4×Dic89 | C4⋊C4 | semidirect |
| 256. #1867 | D89 | semidirect |
| 259. C89 | #12966 | semidirect |
| 316. #99 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023427 | 2 |
| C2×#19151390 | 2 |
| #26020650 | 2 |
| #26020533 | 2 |
| #26018370 | 2 |
| #26018369 | 2 |
| C89×#1867 | 2 |
| #12966 | 89 |