Finite Group DatabasebetaFinite Group DatabasebetaOrder 16832.
310 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 155 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. #22554435 | C2 | semidirect |
| 3. #22554432 | C2 | semidirect |
| 4. (C22⋊D263)⋊C4 | C2 | semidirect |
| 5. #22554427 | C2 | semidirect |
| 6. C2×C4×Dic263 | C2 | semidirect |
| 7. C42×D263 | C2 | semidirect |
| 8. #117×C263 | C2 | semidirect |
| 9. #16862376 | C4 | semidirect |
| 27. Dic526 | C2×C4 | semidirect |
| 28. D1052 | C2×C4 | semidirect |
| 29. C22⋊D263 | C2×C4 | semidirect |
| 35. C4×D263 | C2×C4 | semidirect |
| 37. C2×C4×C263 | C2×C4 | semidirect |
| 51. Dic263 | #41 | semidirect |
| 56. C263 | C4×#41 | semidirect |
| 63. #117 | D263 | semidirect |
| 94. C2×C4 | C4×D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862376 | 2 |
| #22554435 | 2 |
| #22554432 | 2 |
| (C22⋊D263)⋊C4 | 2 |
| #22554427 | 2 |
| C2×C4×Dic263 | 2 |
| C42×D263 | 2 |
| #117×C263 | 2 |
| C4×#41 | 263 |