Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
266 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22553334 | C2 | semidirect |
| 3. C4×#14523496 | C2 | semidirect |
| 4. #22553044 | C2 | semidirect |
| 5. #22553042 | C2 | semidirect |
| 6. D4⋊(C131⋊C8) | C2 | semidirect |
| 7. D4⋊C8×C131 | C2 | semidirect |
| 60. Dic262 | M16 | semidirect |
| 78. D4×C131 | M16 | semidirect |
| 110. C131 | #1489 | semidirect |
| 118. D4⋊C8 | D131 | semidirect |
| 175. D4 | #14523496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523512 | 2 |
| #22553334 | 2 |
| C4×#14523496 | 2 |
| #22553044 | 2 |
| #22553042 | 2 |
| D4⋊(C131⋊C8) | 2 |
| D4⋊C8×C131 | 2 |
| #1489 | 131 |