Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
302 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. #26018434 | C2 | semidirect |
| 5. #26018433 | C2 | semidirect |
| 6. #26018432 | C2 | semidirect |
| 7. C89×#1416 | C2 | semidirect |
| 12. Q32×D89 | C4 | semidirect |
| 30. Dic712 | C2×C4 | semidirect |
| 40. Q32×C89 | C2×C4 | semidirect |
| 101. D89 | #1416 | direct (N × H) |
| 108. #1416 | D89 | direct (N × H) |
| 109. C89 | C2×#1416 | 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×Q32×D89 | 2 |
| C2×C32×D89 | 2 |
| #366×D89 | 2 |
| #26018434 | 2 |
| #26018433 | 2 |
| #26018432 | 2 |
| C89×#1416 | 2 |
| C2×#1416 | 89 |