Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 157 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×#16862277 | C2 | semidirect |
| 3. #22553704 | C2 | semidirect |
| 4. #22553691 | C2 | semidirect |
| 5. #22553686 | C2 | semidirect |
| 6. C4×#14523497 | C2 | semidirect |
| 7. C2×C4⋊Q8×C131 | C2 | semidirect |
| 34. #14523497 | D4 | semidirect |
| 76. C4×C131 | #137 | semidirect |
| 83. C131 | #3152 | semidirect |
| 87. C2×C4⋊Q8 | D131 | semidirect |
| 161. C4 | #16862277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862277 | 2 |
| #22553862 | 2 |
| #22553704 | 2 |
| #22553691 | 2 |
| #22553686 | 2 |
| C4×#14523497 | 2 |
| C2×C4⋊Q8×C131 | 2 |
| #3152 | 131 |