Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
598 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26026193 | C2 | semidirect |
| 3. #26018978 | C2 | semidirect |
| 4. #26018849 | C2 | semidirect |
| 5. #26018760 | C2 | semidirect |
| 6. #26018146 | C2 | semidirect |
| 7. C89×#3152 | C2 | semidirect |
| 192. #3152 | D89 | semidirect |
| 198. C89 | #10090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031235 | 2 |
| #26026193 | 2 |
| #26018978 | 2 |
| #26018849 | 2 |
| #26018760 | 2 |
| #26018146 | 2 |
| C89×#3152 | 2 |
| #10090 | 89 |