Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
928 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 237 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. C2×C4×D524 | C2 | semidirect |
| 3. #22553218 | C2 | semidirect |
| 4. #22553188 | C2 | semidirect |
| 5. #22553174 | C2 | semidirect |
| 6. #22553172 | C2 | semidirect |
| 7. #95×D131 | C2 | semidirect |
| 8. C4×C22⋊C4×C131 | C2 | semidirect |
| 10. C2×#14523513 | C4 | semidirect |
| 31. C2×Dic262 | C2×C4 | semidirect |
| 35. C2×C22⋊D131 | C2×C4 | semidirect |
| 42. C2×C4×D131 | C2×C4 | semidirect |
| 48. C22×C4×C131 | C2×C4 | semidirect |
| 61. D524 | C22⋊C4 | semidirect |
| 86. C2×C4×C131 | #41 | semidirect |
| 115. C131 | #2339 | semidirect |
| 123. C4×C22⋊C4 | D131 | semidirect |
| 161. C22×C4 | C4×D131 | semidirect |
| 202. C2×C4 | #14523513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523513 | 2 |
| C2×C4×D524 | 2 |
| #22553218 | 2 |
| #22553188 | 2 |
| #22553174 | 2 |
| #22553172 | 2 |
| #95×D131 | 2 |
| C4×C22⋊C4×C131 | 2 |
| #2339 | 131 |