Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
628 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 123 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. C4×#15667927 | C2 | semidirect |
| 4. #26018376 | C2 | semidirect |
| 5. C4×#99×C89 | C2 | semidirect |
| 7. C2×C4×D356 | C4 | semidirect |
| 10. #19151499 | C4 | semidirect |
| 15. #19151463 | C4 | semidirect |
| 17. #19151444 | C4 | semidirect |
| 18. #19151390 | C4 | semidirect |
| 43. #15667927 | C2×C4 | semidirect |
| 61. #99×C89 | C2×C4 | semidirect |
| 67. C2×D356 | C42 | semidirect |
| 93. C4×Dic89 | C42 | semidirect |
| 223. C4×#99 | D89 | semidirect |
| 225. C89 | #12628 | semidirect |
| 276. #99 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022974 | 2 |
| C2×#19151390 | 2 |
| C4×#15667927 | 2 |
| #26018376 | 2 |
| C4×#99×C89 | 2 |
| #12628 | 89 |