Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
492 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26019024 | C2 | semidirect |
| 3. #26018921 | C2 | semidirect |
| 4. #26018921 | C2 | semidirect |
| 5. #26018643 | C2 | semidirect |
| 6. #26018147 | C2 | semidirect |
| 7. C89×#1800 | C2 | semidirect |
| 185. #1800 | D89 | semidirect |
| 191. C89 | #10441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151793 | 2 |
| #26019024 | 2 |
| #26018921 | 2 |
| #26018643 | 2 |
| #26018147 | 2 |
| C89×#1800 | 2 |
| #10441 | 89 |