Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
196 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 2. C8×D524 | C2 | semidirect |
| 3. #22553065 | C2 | semidirect |
| 4. #22553041 | C2 | semidirect |
| 5. C82×C131 | C2 | semidirect |
| 18. D1048 | C8 | direct (N × H) |
| 31. D524 | C2×C8 | semidirect |
| 42. C8×C131 | C2×C8 | semidirect |
| 43. C8×C131 | D8 | semidirect |
| 58. C131 | C8×D8 | semidirect |
| 64. C82 | D131 | semidirect |
| 101. C8 | C8×D131 | semidirect |
| 102. C8 | D1048 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1048 | 2 |
| C8×D524 | 2 |
| #22553065 | 2 |
| #22553041 | 2 |
| C82×C131 | 2 |
| C8×D8 | 131 |