Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
596 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 217 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. #22553215 | C2 | semidirect |
| 2. #22553205 | C2 | semidirect |
| 3. #22553198 | C2 | semidirect |
| 4. #22553192 | C2 | semidirect |
| 5. #22553192 | C2 | semidirect |
| 6. #22553175 | C2 | semidirect |
| 7. C22⋊C4×Dic131 | C2 | semidirect |
| 8. C4×C22⋊Dic131 | C2 | semidirect |
| 29. #121×C131 | C4 | semidirect |
| 56. C2×D4×C131 | C2×C4 | semidirect |
| 59. C22×C4×C131 | C2×C4 | semidirect |
| 63. C4⋊C4×C131 | C2×C4 | semidirect |
| 64. C22⋊C4×C131 | C2×C4 | semidirect |
| 134. C131 | #2333 | semidirect |
| 149. #121 | Dic131 | semidirect |
| 174. C2×D4 | C2×Dic131 | semidirect |
| 184. C22×C4 | C2×Dic131 | semidirect |
| 189. C4⋊C4 | C2×Dic131 | semidirect |
| 196. C22⋊C4 | C2×Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553215 | 2 |
| #22553205 | 2 |
| #22553198 | 2 |
| #22553192 | 2 |
| #22553175 | 2 |
| C22⋊C4×Dic131 | 2 |
| C4×C22⋊Dic131 | 2 |
| C2×#121×C131 | 2 |
| #2333 | 131 |