Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
546 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. #26031177 | C2 | semidirect |
| 3. #26030648 | C2 | semidirect |
| 4. #26021170 | C2 | semidirect |
| 5. #26018746 | C2 | semidirect |
| 6. #26018102 | C2 | semidirect |
| 7. C89×#1987 | C2 | semidirect |
| 202. #1987 | D89 | semidirect |
| 206. C89 | #10196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031562 | 2 |
| #26031177 | 2 |
| #26030648 | 2 |
| #26021170 | 2 |
| #26018746 | 2 |
| #26018102 | 2 |
| C89×#1987 | 2 |
| #10196 | 89 |