Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
174 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 81 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. C2×C16×D131 | C2 | semidirect |
| 3. C4⋊(C131⋊C16) | C2 | semidirect |
| 4. (C2×D131)⋊C16 | C2 | semidirect |
| 5. C4×C16×C131 | C2 | semidirect |
| 27. C16×C131 | D4 | semidirect |
| 29. D524 | C16 | direct (N × H) |
| 43. C2×D131 | C2×C16 | semidirect |
| 45. C4×C131 | C2×C16 | semidirect |
| 53. C131 | D4×C16 | semidirect |
| 59. C4×C16 | D131 | semidirect |
| 81. C16 | D524 | direct (N × H) |
| 100. C4 | C16×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D131 | 2 |
| C8×D524 | 2 |
| C4⋊(C131⋊C16) | 2 |
| (C2×D131)⋊C16 | 2 |
| C4×C16×C131 | 2 |
| D4×C16 | 131 |