Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
676 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 189 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×#16862222 | C2 | semidirect |
| 3. #22553247 | C2 | semidirect |
| 5. #22553181 | C2 | semidirect |
| 6. C4×C4⋊Dic131 | C2 | semidirect |
| 7. C2×C4⋊Q8×C131 | C2 | semidirect |
| 27. C2×D524 | Q8 | semidirect |
| 33. C4⋊Dic131 | D4 | semidirect |
| 82. C4×C131 | C22⋊Q8 | semidirect |
| 92. C131 | #2542 | semidirect |
| 94. C2×C4⋊Q8 | D131 | semidirect |
| 177. C4 | #16862222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862222 | 2 |
| C2×C4×D524 | 2 |
| #22553247 | 2 |
| #22553213 | 2 |
| #22553181 | 2 |
| C4×C4⋊Dic131 | 2 |
| C2×C4⋊Q8×C131 | 2 |
| #2542 | 131 |