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. C22×Dic524 | C2 | semidirect |
| 3. C22×#14523503 | C2 | semidirect |
| 4. C2×Q16×D131 | C2 | direct (N × H) |
| 6. C22×Q16×C131 | C2 | semidirect |
| 13. C2×Dic524 | C22 | semidirect |
| 14. C2×#14523503 | C22 | semidirect |
| 15. Q16×D131 | C22 | direct (N × H) |
| 19. C2×Q16×C131 | C22 | semidirect |
| 32. Dic524 | C23 | semidirect |
| 33. #14523503 | C23 | semidirect |
| 40. Q16×C131 | C23 | semidirect |
| 42. C22×D131 | Q16 | direct (N × H) |
| 60. C22×C131 | C2×Q16 | semidirect |
| 62. C2×D131 | C2×Q16 | direct (N × H) |
| 69. C2×C131 | C22×Q16 | semidirect |
| 71. D131 | C22×Q16 | direct (N × H) |
| 72. C131 | C23×Q16 | semidirect |
| 78. C22×Q16 | D131 | direct (N × H) |
| 90. C2×Q16 | C2×D131 | direct (N × H) |
| 111. Q16 | C22×D131 | direct (N × H) |
| 135. C22 | Q16×D131 | direct (N × H) |
| 143. C2 | C2×Q16×D131 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D131 | 2 |
| C22×Dic524 | 2 |
| C22×#14523503 | 2 |
| C2×Q16×D131 | 2 |
| C22×C8×D131 | 2 |
| C22×Q16×C131 | 2 |
| C23×Q16 | 131 |