Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
698 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26024740 | C2 | semidirect |
| 3. #26024719 | C2 | semidirect |
| 4. #26018769 | C2 | semidirect |
| 5. #26018769 | C2 | semidirect |
| 6. #26018137 | C2 | semidirect |
| 7. C89×#1821 | C2 | semidirect |
| 218. #1821 | D89 | semidirect |
| 222. C89 | #10328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031052 | 2 |
| #26024740 | 2 |
| #26024719 | 2 |
| #26018769 | 2 |
| #26018137 | 2 |
| C89×#1821 | 2 |
| #10328 | 89 |