Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
428 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×C4×Dic262 | C2 | semidirect |
| 2. #22553628 | C2 | semidirect |
| 3. #22553594 | C2 | semidirect |
| 4. #22553509 | C2 | semidirect |
| 5. #22553450 | C2 | semidirect |
| 6. C4×#14523501 | C2 | semidirect |
| 7. #22553365 | C2 | semidirect |
| 66. Dic262 | #41 | semidirect |
| 83. C2×C4×C131 | SD16 | semidirect |
| 111. C131 | #3103 | semidirect |
| 194. C2×C4 | #14523501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic262 | 2 |
| #22553628 | 2 |
| #22553594 | 2 |
| #22553509 | 2 |
| #22553450 | 2 |
| C4×#14523501 | 2 |
| #22553365 | 2 |
| #532×C131 | 2 |
| #3103 | 131 |