Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
312 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 11. C2×#14523503 | C4 | semidirect |
| 78. C2×C4×C131 | Q16 | semidirect |
| 104. C131 | #1969 | semidirect |
| 181. C2×C4 | #14523503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523503 | 2 |
| C2×#16862179 | 2 |
| C2×#16862170 | 2 |
| C2×#16862169 | 2 |
| C2×C4×C131⋊C8 | 2 |
| #22553218 | 2 |
| #391×C131 | 2 |
| #1969 | 131 |