Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
680 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 680 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 |
|---|---|---|
| 3. #26020240 | C2 | semidirect |
| 4. #26018376 | C2 | semidirect |
| 5. C89×#1799 | C2 | semidirect |
| 7. C2×C4×D356 | C4 | semidirect |
| 12. #19151499 | C4 | semidirect |
| 15. #19151467 | C4 | semidirect |
| 17. C42×Dic89 | C4 | semidirect |
| 71. C2×D356 | C4⋊C4 | semidirect |
| 103. C4×Dic89 | C4⋊C4 | semidirect |
| 229. C4×C89 | #353 | semidirect |
| 248. #1799 | D89 | semidirect |
| 250. C89 | #12797 | semidirect |
| 478. C4 | #19151390 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668008 | 2 |
| C2×#19151390 | 2 |
| #26020240 | 2 |
| #26018376 | 2 |
| C89×#1799 | 2 |
| #12797 | 89 |