Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16862277 | C2 | semidirect |
| 3. #22553886 | C2 | semidirect |
| 4. #22553705 | C2 | semidirect |
| 5. #22553697 | C2 | semidirect |
| 6. #22553690 | C2 | semidirect |
| 7. #22553267 | C2 | semidirect |
| 8. C22×Q16×C131 | C2 | semidirect |
| 96. C131 | #3156 | semidirect |
| 100. C22×Q16 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862277 | 2 |
| C2×#16862268 | 2 |
| #22553886 | 2 |
| #22553705 | 2 |
| #22553697 | 2 |
| #22553690 | 2 |
| #22553267 | 2 |
| C22×Q16×C131 | 2 |
| #3156 | 131 |