Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
494 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26018815 | C2 | semidirect |
| 4. #26018752 | C2 | semidirect |
| 6. #26018153 | C2 | semidirect |
| 7. C89×#1286 | C2 | semidirect |
| 11. #19151889 | C4 | semidirect |
| 12. #19151879 | C4 | semidirect |
| 197. #1286 | D89 | semidirect |
| 198. C89 | #9177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030051 | 2 |
| #26023227 | 2 |
| #26018815 | 2 |
| #26018752 | 2 |
| #26018642 | 2 |
| #26018153 | 2 |
| C89×#1286 | 2 |
| #9177 | 89 |