Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
238 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. C8×Dic356 | C2 | semidirect |
| 3. #26018323 | C2 | semidirect |
| 4. #26018215 | C2 | semidirect |
| 6. #26018169 | C2 | semidirect |
| 25. #15667956 | C8 | semidirect |
| 46. Dic356 | C2×C8 | semidirect |
| 53. #13083549 | C2×C8 | semidirect |
| 113. C89 | #12043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667956 | 2 |
| C8×Dic356 | 2 |
| #26018323 | 2 |
| #26018215 | 2 |
| #26018213 | 2 |
| #26018169 | 2 |
| C8×D8×C89 | 2 |
| #12043 | 89 |