Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
476 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 213 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. #22553353 | C2 | semidirect |
| 4. #22553352 | C2 | semidirect |
| 5. #22553350 | C2 | semidirect |
| 6. #22553349 | C2 | semidirect |
| 7. #107×D131 | C2 | semidirect |
| 8. C2×#107×C131 | C2 | semidirect |
| 10. #16862252 | C4 | semidirect |
| 36. #14523497 | C2×C4 | semidirect |
| 37. #14523496 | C2×C4 | semidirect |
| 39. C8×D131 | C2×C4 | semidirect |
| 49. C2×C8×C131 | C2×C4 | semidirect |
| 93. C131 | #2913 | semidirect |
| 102. C2×#107 | D131 | semidirect |
| 136. C2×C8 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862252 | 2 |
| #22553793 | 2 |
| #22553353 | 2 |
| #22553352 | 2 |
| #22553350 | 2 |
| #22553349 | 2 |
| #107×D131 | 2 |
| C2×#107×C131 | 2 |
| #2913 | 131 |