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. #22553657 | C2 | semidirect |
| 4. #22553600 | C2 | semidirect |
| 5. #22553599 | C2 | semidirect |
| 6. #22553511 | C2 | semidirect |
| 7. #22553509 | C2 | semidirect |
| 8. C8×Dic262 | C2 | semidirect |
| 9. #22553403 | C2 | semidirect |
| 10. C4×#14523502 | C2 | semidirect |
| 11. #486×C131 | C2 | semidirect |
| 77. Dic262 | SD16 | semidirect |
| 78. Dic262 | #41 | semidirect |
| 125. C131 | #3362 | semidirect |
| 130. #486 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554042 | 2 |
| #22553982 | 2 |
| #22553657 | 2 |
| #22553600 | 2 |
| #22553599 | 2 |
| #22553511 | 2 |
| #22553509 | 2 |
| C8×Dic262 | 2 |
| #22553403 | 2 |
| C4×#14523502 | 2 |
| #486×C131 | 2 |
| #3362 | 131 |