Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
224 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26018325 | C2 | semidirect |
| 5. #26018324 | C2 | semidirect |
| 6. #26018323 | C2 | semidirect |
| 7. C89×#1372 | C2 | semidirect |
| 59. #13083549 | M16 | semidirect |
| 66. C16×C89 | M16 | semidirect |
| 109. #1372 | D89 | semidirect |
| 112. C89 | #12025 | semidirect |
| 171. C16 | #13083557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667951 | 2 |
| #26019014 | 2 |
| #26019009 | 2 |
| #26018325 | 2 |
| #26018324 | 2 |
| #26018323 | 2 |
| C89×#1372 | 2 |
| #12025 | 89 |