Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
480 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 3. #22553522 | C2 | direct (N × H) |
| 64. C2×C4×C131 | Q16 | semidirect |
| 79. C4×C131 | C2×Q16 | semidirect |
| 83. C2×C131 | #462 | semidirect |
| 87. C131 | C2×#462 | semidirect |
| 151. C2×C4 | #14523503 | semidirect |
| 168. C4 | C2×#14523503 | semidirect |
| 171. C2 | #22553522 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523503 | 2 |
| C2×#16862246 | 2 |
| #22553522 | 2 |
| C2×C4⋊(C131⋊C8) | 2 |
| C2×#16862169 | 2 |
| C2×C4×Q8×C131 | 2 |
| C2×#462 | 131 |