Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #22553616 | C2 | semidirect |
| 3. #22553609 | C2 | semidirect |
| 4. #22553352 | C2 | semidirect |
| 5. #22553336 | C2 | semidirect |
| 7. C2×#125×C131 | C2 | semidirect |
| 90. C131 | #3080 | semidirect |
| 92. C2×#125 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523513 | 2 |
| #22553616 | 2 |
| #22553609 | 2 |
| #22553352 | 2 |
| #22553336 | 2 |
| #22553311 | 2 |
| C2×#125×C131 | 2 |
| #3080 | 131 |