Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#14523503 | C2 | semidirect |
| 4. #22553551 | C2 | direct (N × H) |
| 5. C2×#16862179 | C2 | semidirect |
| 6. C2×#16862170 | C2 | semidirect |
| 7. C2×#16862169 | C2 | semidirect |
| 11. C2×#14523503 | C22 | semidirect |
| 21. #16862179 | C22 | semidirect |
| 22. #16862170 | C22 | semidirect |
| 23. #16862169 | C22 | semidirect |
| 75. C23×C131 | Q16 | semidirect |
| 99. C22×C131 | C2×Q16 | semidirect |
| 111. C2×C131 | #467 | semidirect |
| 115. C131 | C2×#467 | semidirect |
| 182. C23 | #14523503 | semidirect |
| 215. C22 | C2×#14523503 | semidirect |
| 227. C2 | #22553551 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523503 | 2 |
| C23×C131⋊C8 | 2 |
| C2×#16862225 | 2 |
| #22553551 | 2 |
| C2×#16862179 | 2 |
| C2×#16862170 | 2 |
| C2×#16862169 | 2 |
| C2×C22⋊Q8×C131 | 2 |
| C2×#467 | 131 |