Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26018817 | C2 | semidirect |
| 4. #26018750 | C2 | semidirect |
| 6. #26018112 | C2 | semidirect |
| 7. C89×#1303 | C2 | semidirect |
| 12. #19151889 | C4 | semidirect |
| 13. #19151879 | C4 | semidirect |
| 32. #15668012 | C2×C4 | semidirect |
| 33. #15668012 | C2×C4 | semidirect |
| 67. C4⋊C8×C89 | C2×C4 | semidirect |
| 201. #1303 | D89 | semidirect |
| 203. C89 | #9175 | semidirect |
| 256. C4⋊C8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030051 | 2 |
| #26023163 | 2 |
| #26018817 | 2 |
| #26018750 | 2 |
| #26018644 | 2 |
| #26018112 | 2 |
| C89×#1303 | 2 |
| #9175 | 89 |