Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
384 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 5. #22553605 | C2 | semidirect |
| 6. #22553520 | C2 | semidirect |
| 8. Q16×Dic131 | C2 | semidirect |
| 9. #22553404 | C2 | semidirect |
| 88. C2×Dic131 | Q16 | semidirect |
| 127. C131 | #3104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553864 | 2 |
| C2×Q8×Dic131 | 2 |
| #22553648 | 2 |
| #22553645 | 2 |
| #22553605 | 2 |
| #22553520 | 2 |
| #22553468 | 2 |
| Q16×Dic131 | 2 |
| #22553404 | 2 |
| #22553362 | 2 |
| #451×C131 | 2 |
| #3104 | 131 |