Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
484 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 153 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. #22553534 | C2 | semidirect |
| 4. #22553522 | C2 | semidirect |
| 5. #22553512 | C2 | semidirect |
| 6. #22553336 | C2 | semidirect |
| 7. #22553311 | C2 | semidirect |
| 8. C2×C4×Q8×C131 | C2 | semidirect |
| 52. C2×Q8×C131 | D4 | semidirect |
| 111. C4×C131 | #137 | semidirect |
| 120. C131 | #3037 | semidirect |
| 124. C2×C4×Q8 | D131 | semidirect |
| 160. C2×Q8 | D524 | semidirect |
| 233. 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 |
| #22553534 | 2 |
| #22553522 | 2 |
| #22553512 | 2 |
| #22553336 | 2 |
| #22553311 | 2 |
| C2×C4×Q8×C131 | 2 |
| #3037 | 131 |