Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
872 conjugacy classes of subgroups; only the 313 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 313 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×Q8×Dic131 | C2 | semidirect |
| 2. #22553215 | C2 | semidirect |
| 3. #22553172 | C2 | semidirect |
| 4. C4×C22⋊Dic131 | C2 | semidirect |
| 14. C2×#41×C131 | C4 | semidirect |
| 39. C2×Dic131 | #41 | semidirect |
| 46. Q8×C131 | C22⋊C4 | semidirect |
| 73. C131 | #2341 | semidirect |
| 81. C2×#41 | Dic131 | semidirect |
| 114. Q8 | C22⋊Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic131 | 2 |
| #22553215 | 2 |
| #22553172 | 2 |
| C4×C22⋊Dic131 | 2 |
| C22×#41×C131 | 2 |
| #2341 | 131 |