Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
740 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26021385 | C2 | semidirect |
| 3. #26018073 | C2 | semidirect |
| 4. #26018072 | C2 | semidirect |
| 5. C89×#2013 | C2 | semidirect |
| 13. #19151353 | C22 | semidirect |
| 15. C2×C4⋊Q8×C89 | C22 | semidirect |
| 18. #336×C89 | C22 | semidirect |
| 58. C2×D356 | SD16 | semidirect |
| 179. #2013 | D89 | semidirect |
| 182. C89 | #7750 | semidirect |
| 184. C2×C4⋊Q8 | C2×D89 | semidirect |
| 195. #336 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026587 | 2 |
| #26021385 | 2 |
| #26018073 | 2 |
| #26018072 | 2 |
| C89×#2013 | 2 |
| #7750 | 89 |