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 |
|---|---|---|
| 2. C2×C4×Dic262 | C2 | semidirect |
| 3. #22553631 | C2 | semidirect |
| 4. #22553598 | C2 | semidirect |
| 5. #22553513 | C2 | semidirect |
| 6. #22553453 | C2 | semidirect |
| 7. C4×#14523502 | C2 | semidirect |
| 8. #431×C131 | C2 | semidirect |
| 68. Dic262 | #41 | semidirect |
| 82. C2×C4×C131 | SD16 | semidirect |
| 111. C131 | #3103 | semidirect |
| 120. #431 | D131 | semidirect |
| 194. C2×C4 | #14523502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553862 | 2 |
| C2×C4×Dic262 | 2 |
| #22553631 | 2 |
| #22553598 | 2 |
| #22553513 | 2 |
| #22553453 | 2 |
| C4×#14523502 | 2 |
| #431×C131 | 2 |
| #3103 | 131 |