Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
672 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 672 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. #26020535 | C2 | semidirect |
| 5. #26020532 | C2 | semidirect |
| 6. #26018371 | C2 | semidirect |
| 7. C89×#1390 | C2 | semidirect |
| 21. #19151390 | C4 | semidirect |
| 60. #15667927 | C2×C4 | semidirect |
| 73. #99×C89 | C2×C4 | semidirect |
| 79. C2×D356 | C4⋊C4 | semidirect |
| 121. C4×Dic89 | C4⋊C4 | semidirect |
| 264. #1390 | D89 | semidirect |
| 265. C89 | #12964 | semidirect |
| 328. #99 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023315 | 2 |
| C2×#19151390 | 2 |
| #26020648 | 2 |
| #26020535 | 2 |
| #26020532 | 2 |
| #26018371 | 2 |
| C89×#1390 | 2 |
| #12964 | 89 |