Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
656 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 213 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×#14523502 | C2 | semidirect |
| 2. C2×#16862246 | C2 | semidirect |
| 4. #22553685 | C2 | direct (N × H) |
| 5. C2×C4×C8×C131 | C2 | semidirect |
| 10. C2×#14523502 | C22 | semidirect |
| 12. #16862246 | C22 | semidirect |
| 18. C4×C8×C131 | C22 | semidirect |
| 33. C2×C8×C131 | D4 | semidirect |
| 48. C2×C4×C131 | SD16 | semidirect |
| 53. C8×C131 | C2×D4 | semidirect |
| 61. C4×C131 | C2×SD16 | semidirect |
| 64. C2×C131 | #492 | semidirect |
| 68. C131 | C2×#492 | semidirect |
| 74. C2×C4×C8 | D131 | semidirect |
| 87. C4×C8 | C2×D131 | semidirect |
| 101. C2×C8 | D524 | semidirect |
| 117. C2×C4 | #14523502 | semidirect |
| 122. C8 | C2×D524 | semidirect |
| 131. C4 | C2×#14523502 | semidirect |
| 134. C2 | #22553685 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523502 | 2 |
| C2×#16862246 | 2 |
| C2×#16862243 | 2 |
| #22553685 | 2 |
| C2×C4×C8×C131 | 2 |
| C2×#492 | 131 |