Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
364 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 364 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 |
|---|---|---|
| 1. #26022423 | C2 | semidirect |
| 2. #26019878 | C2 | semidirect |
| 3. #26018289 | C2 | semidirect |
| 4. #26018228 | C2 | semidirect |
| 6. #19151996 | C22 | semidirect |
| 10. #19151419 | C22 | semidirect |
| 12. #19151319 | C22 | semidirect |
| 60. Q16×C89 | SD16 | semidirect |
| 68. D8×C89 | SD16 | semidirect |
| 121. C89 | #12366 | semidirect |
| 171. Q16 | #13083562 | semidirect |
| 180. D8 | #13083562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022423 | 2 |
| #26019878 | 2 |
| #26018289 | 2 |
| #26018228 | 2 |
| C89×#3292 | 2 |
| #12366 | 89 |