Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 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. #22553943 | C2 | semidirect |
| 3. #22553618 | C2 | semidirect |
| 4. #22553615 | C2 | semidirect |
| 5. #22553606 | C2 | semidirect |
| 6. #22553591 | C2 | semidirect |
| 7. #22553352 | C2 | semidirect |
| 8. #22553338 | C2 | semidirect |
| 11. C2×#107×C131 | C2 | semidirect |
| 42. #14523513 | Q8 | semidirect |
| 123. C131 | #3083 | semidirect |
| 132. C2×#107 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553943 | 2 |
| #22553793 | 2 |
| #22553618 | 2 |
| #22553615 | 2 |
| #22553606 | 2 |
| #22553591 | 2 |
| #22553352 | 2 |
| #22553338 | 2 |
| #22553311 | 2 |
| #22553309 | 2 |
| C2×#107×C131 | 2 |
| #3083 | 131 |