Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
428 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 127 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. C4×Q8×D131 | C2 | semidirect |
| 3. #22553629 | C2 | semidirect |
| 4. #22553598 | C2 | semidirect |
| 5. #22553597 | C2 | semidirect |
| 6. #22553509 | C2 | semidirect |
| 7. #22553449 | C2 | semidirect |
| 8. #22553403 | C2 | semidirect |
| 9. SD16×Dic131 | C2 | semidirect |
| 10. #22553364 | C2 | semidirect |
| 11. #460×C131 | C2 | semidirect |
| 87. Dic262 | #41 | semidirect |
| 101. C4×D131 | SD16 | semidirect |
| 105. Q8×C131 | #41 | semidirect |
| 140. C131 | #3103 | semidirect |
| 148. #460 | D131 | semidirect |
| 231. Q8 | #14523512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553860 | 2 |
| C4×Q8×D131 | 2 |
| #22553629 | 2 |
| #22553598 | 2 |
| #22553597 | 2 |
| #22553509 | 2 |
| #22553449 | 2 |
| #22553403 | 2 |
| SD16×Dic131 | 2 |
| #22553364 | 2 |
| #460×C131 | 2 |
| #3103 | 131 |