Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
258 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 258 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 |
|---|---|---|
| 2. C8×D712 | C2 | semidirect |
| 3. #26018323 | C2 | semidirect |
| 4. #26018213 | C2 | semidirect |
| 5. #26018212 | C2 | semidirect |
| 6. C8×#13083549 | C2 | semidirect |
| 7. C8×D8×C89 | C2 | semidirect |
| 26. #15667953 | C8 | direct (N × H) |
| 47. D712 | C2×C8 | semidirect |
| 54. #13083549 | C2×C8 | semidirect |
| 58. D8×C89 | C2×C8 | semidirect |
| 88. C8×C89 | D16 | semidirect |
| 114. C8×D8 | D89 | semidirect |
| 119. C89 | C8×D16 | semidirect |
| 163. D8 | C8×D89 | semidirect |
| 201. C8 | #15667953 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667953 | 2 |
| C8×D712 | 2 |
| #26018323 | 2 |
| #26018213 | 2 |
| #26018212 | 2 |
| C8×#13083549 | 2 |
| C8×D8×C89 | 2 |
| C8×D16 | 89 |