Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1464 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 565 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×#16862277 | C2 | direct (N × H) |
| 3. C22×#14523503 | C2 | semidirect |
| 4. C22×#14523500 | C2 | semidirect |
| 5. C22×#14523497 | C2 | semidirect |
| 6. C23×Q8×C131 | C2 | semidirect |
| 13. #16862277 | C22 | direct (N × H) |
| 14. C2×#14523503 | C22 | semidirect |
| 15. C2×#14523500 | C22 | semidirect |
| 16. C2×#14523497 | C22 | semidirect |
| 21. C22×Q8×C131 | C22 | semidirect |
| 34. #14523503 | C23 | semidirect |
| 35. #14523500 | C23 | semidirect |
| 36. #14523497 | C23 | semidirect |
| 43. C2×Q8×C131 | C23 | semidirect |
| 74. C22×C131 | #137 | semidirect |
| 85. C2×C131 | C2×#137 | semidirect |
| 88. C131 | C22×#137 | semidirect |
| 91. C23×Q8 | D131 | semidirect |
| 102. C22×Q8 | C2×D131 | semidirect |
| 123. C2×Q8 | C22×D131 | semidirect |
| 165. C22 | #16862277 | direct (N × H) |
| 175. C2 | C2×#16862277 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523513 | 2 |
| C2×#16862277 | 2 |
| C22×#14523503 | 2 |
| C22×#14523500 | 2 |
| C22×#14523497 | 2 |
| C23×Q8×C131 | 2 |
| C22×#137 | 131 |