Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
640 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26031190 | C2 | semidirect |
| 3. #26021197 | C2 | semidirect |
| 4. #26021178 | C2 | semidirect |
| 5. #26018747 | C2 | semidirect |
| 6. #26018102 | C2 | semidirect |
| 7. C89×#3246 | C2 | semidirect |
| 95. #13083558 | SD16 | semidirect |
| 210. #3246 | D89 | semidirect |
| 217. C89 | #10194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031190 | 2 |
| #26030705 | 2 |
| #26021197 | 2 |
| #26021178 | 2 |
| #26018747 | 2 |
| #26018102 | 2 |
| C89×#3246 | 2 |
| #10194 | 89 |