Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
276 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 101 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×C4×C131⋊C8 | C2 | semidirect |
| 3. #22553042 | C2 | semidirect |
| 4. #22553039 | C2 | semidirect |
| 5. #431×C131 | C2 | semidirect |
| 24. #14523513 | C8 | semidirect |
| 53. Dic262 | C2×C8 | semidirect |
| 55. D524 | C2×C8 | semidirect |
| 98. C131 | #1476 | semidirect |
| 101. #431 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523513 | 2 |
| C2×C4×C131⋊C8 | 2 |
| #22553042 | 2 |
| #22553039 | 2 |
| #431×C131 | 2 |
| #1476 | 131 |