Finite Group DatabasebetaFinite Group DatabasebetaOrder 16832.
188 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 47 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. C2×#16862365 | C2 | semidirect |
| 3. #22554449 | C2 | semidirect |
| 4. #22554392 | C2 | semidirect |
| 5. C22⋊C8×C263 | C2 | semidirect |
| 7. C2×Dic526 | C22 | semidirect |
| 12. C4⋊Dic263 | C22 | semidirect |
| 16. C2×C8×C263 | C22 | semidirect |
| 34. C22×C263 | SD16 | semidirect |
| 49. C263 | #450 | semidirect |
| 55. C22⋊C8 | D263 | semidirect |
| 63. C2×C8 | C2×D263 | semidirect |
| 88. C22 | #16862365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1052 | 2 |
| C2×#16862365 | 2 |
| #22554449 | 2 |
| #22554392 | 2 |
| C22⋊C8×C263 | 2 |
| #450 | 263 |