Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
456 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 173 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. #22553207 | C2 | semidirect |
| 4. #22553193 | C2 | semidirect |
| 6. #22553180 | C2 | semidirect |
| 7. #384×C131 | C2 | semidirect |
| 9. #16862240 | C4 | semidirect |
| 28. Dic131⋊C4 | C2×C4 | semidirect |
| 37. C42×C131 | C2×C4 | semidirect |
| 72. C131 | #2383 | semidirect |
| 79. #384 | D131 | semidirect |
| 110. C42 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862240 | 2 |
| #22553207 | 2 |
| #22553202 | 2 |
| #22553193 | 2 |
| #22553183 | 2 |
| #22553180 | 2 |
| #384×C131 | 2 |
| #2383 | 131 |