Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#19151431 | C2 | semidirect |
| 3. #366×D89 | C2 | semidirect |
| 4. #26018433 | C2 | semidirect |
| 5. #26018431 | C2 | semidirect |
| 6. #26018429 | C2 | semidirect |
| 7. C89×#1416 | C2 | semidirect |
| 10. #19152031 | C4 | semidirect |
| 31. D1424 | C2×C4 | semidirect |
| 40. Q32×C89 | C2×C4 | semidirect |
| 109. #1416 | D89 | semidirect |
| 112. C89 | #13616 | semidirect |
| 136. Q32 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152031 | 2 |
| C2×#19151431 | 2 |
| #366×D89 | 2 |
| #26018433 | 2 |
| #26018431 | 2 |
| #26018429 | 2 |
| C89×#1416 | 2 |
| #13616 | 89 |