Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
194 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. #26022129 | C2 | semidirect |
| 3. #26018459 | C2 | semidirect |
| 4. #26018441 | C2 | semidirect |
| 5. #26018439 | C2 | semidirect |
| 6. #26018388 | C2 | semidirect |
| 7. C89×#2179 | C2 | semidirect |
| 10. #19151435 | C4 | semidirect |
| 11. #19151433 | C4 | semidirect |
| 28. #15667918 | C2×C4 | semidirect |
| 31. Q32×C89 | C2×C4 | semidirect |
| 33. D16×C89 | C2×C4 | semidirect |
| 89. #2179 | D89 | semidirect |
| 95. C89 | #13658 | semidirect |
| 113. Q32 | C4×D89 | semidirect |
| 117. D16 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022564 | 2 |
| #26022129 | 2 |
| #26018459 | 2 |
| #26018441 | 2 |
| #26018439 | 2 |
| #26018388 | 2 |
| C89×#2179 | 2 |
| #13658 | 89 |