Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 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×#16862185 | C2 | semidirect |
| 3. (C2×D131)⋊C16 | C2 | semidirect |
| 4. C4×C131⋊C16 | C2 | semidirect |
| 5. C4⋊C16×C131 | C2 | semidirect |
| 23. C131⋊C16 | D4 | semidirect |
| 45. C4×C131 | M32 | semidirect |
| 53. C131 | #2169 | semidirect |
| 57. C4⋊C16 | D131 | semidirect |
| 100. C4 | #16862185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862185 | 2 |
| C8×D524 | 2 |
| (C2×D131)⋊C16 | 2 |
| C4×C131⋊C16 | 2 |
| C4⋊C16×C131 | 2 |
| #2169 | 131 |