Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 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 |
|---|---|---|
| 3. #20292978 | C2 | semidirect |
| 4. #20292963 | C2 | semidirect |
| 5. #20292923 | C2 | semidirect |
| 6. #20292868 | C2 | semidirect |
| 7. #20292838 | C2 | semidirect |
| 8. #20292785 | C2 | semidirect |
| 9. C4×Dic428 | C2 | semidirect |
| 10. C2×#16812034 | C2 | semidirect |
| 77. D4×C107 | Q16 | semidirect |
| 123. C107 | #3299 | semidirect |
| 208. D4 | Dic428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293334 | 2 |
| D4×Dic214 | 2 |
| #20292978 | 2 |
| #20292963 | 2 |
| #20292923 | 2 |
| #20292868 | 2 |
| #20292838 | 2 |
| #20292785 | 2 |
| C4×Dic428 | 2 |
| C2×#16812034 | 2 |
| C8×D4×C107 | 2 |
| #3299 | 107 |