Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
360 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26022064 | C2 | semidirect |
| 2. #26018555 | C2 | semidirect |
| 3. #26018228 | C2 | semidirect |
| 4. #26018225 | C2 | semidirect |
| 7. #19151419 | C22 | semidirect |
| 11. #19151319 | C22 | semidirect |
| 12. C8×#10623494 | C22 | semidirect |
| 63. Q16×C89 | M16 | semidirect |
| 67. D8×C89 | M16 | semidirect |
| 130. C89 | #11669 | semidirect |
| 184. Q16 | #13083558 | semidirect |
| 188. D8 | #13083558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022064 | 2 |
| #26018555 | 2 |
| #26018228 | 2 |
| #26018225 | 2 |
| C89×#2956 | 2 |
| #11669 | 89 |