Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 3. Q16×#10623494 | C2 | semidirect |
| 4. #26018315 | C2 | semidirect |
| 5. #26018310 | C2 | semidirect |
| 7. C89×#2227 | C2 | semidirect |
| 60. Q16×C89 | SD16 | semidirect |
| 109. #2227 | D89 | semidirect |
| 116. C89 | #12419 | semidirect |
| 160. Q16 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022292 | 2 |
| #26019845 | 2 |
| Q16×#10623494 | 2 |
| #26018315 | 2 |
| #26018310 | 2 |
| #26018299 | 2 |
| C89×#2227 | 2 |
| #12419 | 89 |