Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
294 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 61 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. C2×Q32×D89 | C2 | semidirect |
| 2. C2×#19151437 | C2 | semidirect |
| 3. C2×#19151435 | C2 | semidirect |
| 5. #26018432 | C2 | semidirect |
| 6. #26018389 | C2 | semidirect |
| 7. C89×#1416 | C2 | semidirect |
| 32. Dic712 | D4 | semidirect |
| 43. Q32×C89 | D4 | semidirect |
| 99. C2×D89 | SD64 | semidirect |
| 117. #1416 | D89 | semidirect |
| 119. C89 | #13662 | semidirect |
| 148. Q32 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D89 | 2 |
| C2×#19151437 | 2 |
| C2×#19151435 | 2 |
| #26022339 | 2 |
| #26018432 | 2 |
| #26018389 | 2 |
| C89×#1416 | 2 |
| #13662 | 89 |