Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
242 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #26018326 | C2 | semidirect |
| 5. #26018325 | C2 | semidirect |
| 6. #26018323 | C2 | semidirect |
| 7. C89×#1371 | C2 | semidirect |
| 28. #15667951 | C8 | semidirect |
| 59. #13083549 | C2×C8 | semidirect |
| 66. C16×C89 | C2×C8 | semidirect |
| 111. #1371 | D89 | semidirect |
| 112. C89 | #12009 | semidirect |
| 171. C16 | C8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667951 | 2 |
| #26018999 | 2 |
| #335×D89 | 2 |
| #26018326 | 2 |
| #26018325 | 2 |
| #26018323 | 2 |
| C89×#1371 | 2 |
| #12009 | 89 |