Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
| 2. C2×#16862252 | C2 | semidirect |
| 4. #22553886 | C2 | semidirect |
| 5. #22553569 | C2 | semidirect |
| 6. #22553561 | C2 | semidirect |
| 7. #22553552 | C2 | semidirect |
| 8. #22553544 | C2 | semidirect |
| 9. #22553352 | C2 | semidirect |
| 10. #22553309 | C2 | semidirect |
| 11. C2×#103×C131 | C2 | semidirect |
| 58. #14523497 | D4 | semidirect |
| 143. C131 | #3063 | semidirect |
| 155. C2×#103 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862277 | 2 |
| C2×#16862252 | 2 |
| #22553893 | 2 |
| #22553886 | 2 |
| #22553569 | 2 |
| #22553561 | 2 |
| #22553552 | 2 |
| #22553544 | 2 |
| #22553352 | 2 |
| #22553309 | 2 |
| C2×#103×C131 | 2 |
| #3063 | 131 |