Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic262 | C2 | semidirect |
| 3. #22553663 | C2 | semidirect |
| 4. #22553643 | C2 | semidirect |
| 5. #22553598 | C2 | semidirect |
| 6. #22553541 | C2 | semidirect |
| 7. #22553518 | C2 | semidirect |
| 8. #22553453 | C2 | semidirect |
| 9. C4×#14523502 | C2 | semidirect |
| 10. C2×#16862171 | C2 | semidirect |
| 11. C8×D4×C131 | C2 | semidirect |
| 83. Dic262 | #41 | semidirect |
| 96. D4×C131 | SD16 | semidirect |
| 128. C131 | #3298 | semidirect |
| 139. C8×D4 | D131 | semidirect |
| 217. D4 | #14523502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic262 | 2 |
| #22553966 | 2 |
| #22553663 | 2 |
| #22553643 | 2 |
| #22553598 | 2 |
| #22553541 | 2 |
| #22553518 | 2 |
| #22553453 | 2 |
| C4×#14523502 | 2 |
| C2×#16862171 | 2 |
| C8×D4×C131 | 2 |
| #3298 | 131 |