Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#16862276 | C2 | semidirect |
| 2. C2×C4×Dic262 | C2 | semidirect |
| 3. #22553531 | C2 | semidirect |
| 4. #22553519 | C2 | semidirect |
| 5. #22553509 | C2 | semidirect |
| 6. #22553336 | C2 | semidirect |
| 7. #22553313 | C2 | semidirect |
| 36. C2×Dic262 | D4 | semidirect |
| 110. C4×C131 | #137 | semidirect |
| 120. C131 | #3037 | semidirect |
| 233. C4 | #16862276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862276 | 2 |
| C2×C4×Dic262 | 2 |
| #22553531 | 2 |
| #22553519 | 2 |
| #22553509 | 2 |
| #22553336 | 2 |
| #22553313 | 2 |
| #532×C131 | 2 |
| #3037 | 131 |