Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1464 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 525 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. C22×Q8×D131 | C2 | semidirect |
| 3. C2×#16862278 | C2 | direct (N × H) |
| 4. C22×#14523503 | C2 | semidirect |
| 5. C22×#14523502 | C2 | semidirect |
| 6. C22×#14523500 | C2 | semidirect |
| 7. C22×#14523496 | C2 | semidirect |
| 8. C22×Q16×C131 | C2 | semidirect |
| 14. C2×Q8×D131 | C22 | semidirect |
| 20. #16862278 | C22 | direct (N × H) |
| 21. C2×#14523503 | C22 | semidirect |
| 22. C2×#14523502 | C22 | semidirect |
| 23. C2×#14523500 | C22 | semidirect |
| 24. C2×#14523496 | C22 | semidirect |
| 28. C2×Q16×C131 | C22 | semidirect |
| 38. Q8×D131 | C23 | semidirect |
| 48. #14523503 | C23 | semidirect |
| 49. #14523502 | C23 | semidirect |
| 50. #14523500 | C23 | semidirect |
| 51. #14523496 | C23 | semidirect |
| 60. Q16×C131 | C23 | semidirect |
| 89. C22×C131 | #137 | semidirect |
| 101. C2×C131 | C2×#137 | semidirect |
| 105. C131 | C22×#137 | semidirect |
| 111. C22×Q16 | D131 | semidirect |
| 130. C2×Q16 | C2×D131 | semidirect |
| 162. Q16 | C22×D131 | semidirect |
| 199. C22 | #16862278 | direct (N × H) |
| 209. C2 | C2×#16862278 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523514 | 2 |
| C22×Q8×D131 | 2 |
| C2×#16862278 | 2 |
| C22×#14523503 | 2 |
| C22×#14523502 | 2 |
| C22×#14523500 | 2 |
| C22×#14523496 | 2 |
| C22×Q16×C131 | 2 |
| C22×#137 | 131 |