Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
486 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 486 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 |
|---|---|---|
| 4. C2×#19151375 | C2 | semidirect |
| 5. #26020138 | C2 | semidirect |
| 6. #26018350 | C2 | semidirect |
| 7. C89×#1386 | C2 | semidirect |
| 12. #19151709 | C4 | semidirect |
| 17. #19151412 | C4 | semidirect |
| 18. #19151398 | C4 | semidirect |
| 40. C2×#13083549 | C2×C4 | semidirect |
| 42. #15667948 | C2×C4 | semidirect |
| 52. M32×C89 | C2×C4 | semidirect |
| 54. #107×C89 | C2×C4 | semidirect |
| 151. #1386 | D89 | semidirect |
| 153. C89 | #12647 | semidirect |
| 190. M32 | C4×D89 | semidirect |
| 195. #107 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151709 | 2 |
| C2×#19151412 | 2 |
| #26021967 | 2 |
| C2×#19151375 | 2 |
| #26020138 | 2 |
| #26018350 | 2 |
| C89×#1386 | 2 |
| #12647 | 89 |