Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
536 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 536 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. #26018078 | C2 | semidirect |
| 5. #26018078 | C2 | semidirect |
| 6. #26018075 | C2 | semidirect |
| 7. C89×#2806 | C2 | semidirect |
| 102. C2×Q8×C89 | SD16 | semidirect |
| 122. C4⋊C4×C89 | SD16 | semidirect |
| 217. #2806 | D89 | semidirect |
| 224. C89 | #7748 | semidirect |
| 290. C2×Q8 | #13083561 | semidirect |
| 339. C4⋊C4 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021486 | 2 |
| #26021339 | 2 |
| #26018078 | 2 |
| #26018075 | 2 |
| C89×#2806 | 2 |
| #7748 | 89 |