Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 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×#16862246 | C2 | semidirect |
| 3. #22553522 | C2 | semidirect |
| 4. #22553517 | C2 | semidirect |
| 5. #22553336 | C2 | semidirect |
| 6. #22553320 | C2 | semidirect |
| 89. C4×C131 | #137 | semidirect |
| 97. C131 | #3039 | semidirect |
| 188. 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×#16862246 | 2 |
| #22553522 | 2 |
| #22553517 | 2 |
| #22553336 | 2 |
| #22553320 | 2 |
| C4×#41×C131 | 2 |
| #3039 | 131 |