Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
424 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #26019043 | C2 | semidirect |
| 5. #26018673 | C2 | semidirect |
| 6. #26018141 | C2 | semidirect |
| 7. C89×#1561 | C2 | semidirect |
| 168. #1561 | D89 | semidirect |
| 172. C89 | #10492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031190 | 2 |
| #26021091 | 2 |
| #26019043 | 2 |
| #26018921 | 2 |
| #26018673 | 2 |
| #26018141 | 2 |
| C89×#1561 | 2 |
| #10492 | 89 |