Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
392 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 1. #22554042 | C2 | semidirect |
| 3. #22553660 | C2 | semidirect |
| 4. #22553657 | C2 | semidirect |
| 5. #22553601 | C2 | semidirect |
| 6. #22553513 | C2 | semidirect |
| 7. #22553511 | C2 | semidirect |
| 8. #22553436 | C2 | semidirect |
| 9. #22553399 | C2 | semidirect |
| 10. C4×#14523501 | C2 | semidirect |
| 11. #476×C131 | C2 | semidirect |
| 77. Dic262 | SD16 | semidirect |
| 78. Dic262 | #41 | semidirect |
| 125. C131 | #3362 | semidirect |
| 132. #476 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554042 | 2 |
| #22553983 | 2 |
| #22553660 | 2 |
| #22553657 | 2 |
| #22553601 | 2 |
| #22553513 | 2 |
| #22553511 | 2 |
| #22553436 | 2 |
| #22553399 | 2 |
| C4×#14523501 | 2 |
| #476×C131 | 2 |
| #3362 | 131 |