Finite Group DatabasebetaFinite Group DatabasebetaOrder 16832.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 1. #22554464 | C2 | semidirect |
| 2. #22554462 | C2 | semidirect |
| 3. #22554458 | C2 | semidirect |
| 4. #22554453 | C2 | semidirect |
| 5. #22554449 | C2 | semidirect |
| 7. C4×Dic526 | C2 | semidirect |
| 8. C4×D1052 | C2 | semidirect |
| 9. C4×C22⋊D263 | C2 | semidirect |
| 10. #22554427 | C2 | semidirect |
| 11. C2×C42×C263 | C2 | semidirect |
| 74. C263 | #529 | semidirect |
| 86. C2×C42 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554464 | 2 |
| #22554462 | 2 |
| #22554458 | 2 |
| #22554453 | 2 |
| #22554449 | 2 |
| #22554444 | 2 |
| C4×Dic526 | 2 |
| C4×D1052 | 2 |
| C4×C22⋊D263 | 2 |
| #22554427 | 2 |
| C2×C42×C263 | 2 |
| #529 | 263 |