Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
612 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 612 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 |
|---|---|---|
| 3. #26021195 | C2 | semidirect |
| 4. #26018765 | C2 | semidirect |
| 6. #26018144 | C2 | semidirect |
| 7. C89×#1285 | C2 | semidirect |
| 12. #19151879 | C4 | semidirect |
| 13. #19151804 | C4 | semidirect |
| 34. #15668012 | C2×C4 | semidirect |
| 35. #15668012 | C2×C4 | semidirect |
| 65. C4⋊C8×C89 | C2×C4 | semidirect |
| 192. #1285 | D89 | semidirect |
| 193. C89 | #9323 | semidirect |
| 243. C4⋊C8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030352 | 2 |
| #26022612 | 2 |
| #26021195 | 2 |
| #26018765 | 2 |
| #26018694 | 2 |
| #26018144 | 2 |
| C89×#1285 | 2 |
| #9323 | 89 |