Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
3550 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 667 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 |
|---|---|---|
| 1. #26028505 | C2 | direct (N × H) |
| 2. C2×#19151510 | C2 | semidirect |
| 5. C23×Dic178 | C22 | semidirect |
| 7. #19151510 | C22 | semidirect |
| 9. C2×#15667919 | C22 | semidirect |
| 14. C22×Dic178 | C23 | semidirect |
| 18. #15667919 | C23 | semidirect |
| 20. C25×C89 | Q8 | semidirect |
| 37. C24×C89 | C2×Q8 | semidirect |
| 73. C2×C89 | #2840 | semidirect |
| 80. C89 | C2×#2840 | semidirect |
| 90. C25 | Dic178 | semidirect |
| 108. C24 | C2×Dic178 | semidirect |
| 148. C2 | #26028505 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028505 | 2 |
| C2×#19151510 | 2 |
| C2×#19151454 | 2 |
| C2×#379×C89 | 2 |
| C2×#2840 | 89 |