Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
200 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22553065 | C2 | direct (N × H) |
| 18. C2×C8×C131 | C8 | semidirect |
| 39. C8×C131 | C2×C8 | semidirect |
| 52. C2×C131 | #335 | semidirect |
| 56. C131 | C2×#335 | semidirect |
| 75. C2×C8 | C131⋊C8 | semidirect |
| 96. C8 | C2×C131⋊C8 | semidirect |
| 109. C2 | #22553065 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C131⋊C8) | 2 |
| #22553065 | 2 |
| C2×C4×C8×C131 | 2 |
| C2×#335 | 131 |