Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
704 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 233 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 |
|---|---|---|
| 3. #22553208 | C2 | semidirect |
| 4. #22553186 | C2 | semidirect |
| 5. #22553171 | C2 | semidirect |
| 6. C4×C4⋊Dic131 | C2 | semidirect |
| 7. #95×D131 | C2 | semidirect |
| 8. #382×C131 | C2 | semidirect |
| 12. C4×D524 | C4 | semidirect |
| 38. C2×C4×D131 | C2×C4 | semidirect |
| 40. C4⋊Dic131 | C2×C4 | semidirect |
| 43. (C2×D131)⋊C4 | C2×C4 | semidirect |
| 50. C42×C131 | C2×C4 | semidirect |
| 56. D524 | C4⋊C4 | semidirect |
| 101. C131 | #2349 | semidirect |
| 107. #382 | D131 | semidirect |
| 152. C42 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D524 | 2 |
| C2×#16862208 | 2 |
| #22553208 | 2 |
| #22553186 | 2 |
| #22553171 | 2 |
| C4×C4⋊Dic131 | 2 |
| #95×D131 | 2 |
| #382×C131 | 2 |
| #2349 | 131 |