Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
732 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 259 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. #26020809 | C2 | semidirect |
| 4. #26020395 | C2 | semidirect |
| 5. #26020126 | C2 | semidirect |
| 7. C42×C8×C89 | C2 | semidirect |
| 76. C42×C89 | M16 | semidirect |
| 99. C8×C89 | #126 | semidirect |
| 126. C42×C8 | D89 | semidirect |
| 127. C89 | #21666 | semidirect |
| 196. C42 | #13083557 | semidirect |
| 221. C8 | #15668006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668006 | 2 |
| #26020858 | 2 |
| #26020809 | 2 |
| #26020395 | 2 |
| #26020126 | 2 |
| #26020035 | 2 |
| C42×C8×C89 | 2 |
| #21666 | 89 |