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 |
|---|---|---|
| 1. C2×#16862246 | C2 | semidirect |
| 2. #22553592 | C2 | direct (N × H) |
| 3. C2×#16862179 | C2 | semidirect |
| 4. C2×C4⋊(C131⋊C8) | C2 | semidirect |
| 10. #16862246 | C22 | semidirect |
| 13. #16862179 | C22 | semidirect |
| 14. C4⋊(C131⋊C8) | C22 | semidirect |
| 34. C2×D4×C131 | Q8 | semidirect |
| 58. D4×C131 | C2×Q8 | semidirect |
| 86. C2×C131 | #474 | semidirect |
| 90. C131 | C2×#474 | semidirect |
| 119. C2×D4 | Dic262 | semidirect |
| 146. D4 | C2×Dic262 | semidirect |
| 177. C2 | #22553592 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862246 | 2 |
| #22553592 | 2 |
| C2×#16862179 | 2 |
| C2×C4⋊(C131⋊C8) | 2 |
| C2×#16862167 | 2 |
| C2×C4×D4×C131 | 2 |
| C2×#474 | 131 |